2024

STEMscopes Math

Publisher
Accelerate Learning
Subject
Math
Grades
K-8
Report Release
10/16/2024
Review Tool Version
v1.5
Format
Core: Comprehensive

EdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.

Alignment (Gateway 1 & 2)
Meets Expectations

Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.

Usability (Gateway 3)
Meets Expectations
Our Review Process

Learn more about EdReports’ educator-led review process

Learn More

About This Report

Report for 6th Grade

Alignment Summary

The materials reviewed for STEMscopes Math Grade 6 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and meet expectations for practice-content connections.

6th Grade
Alignment (Gateway 1 & 2)
Meets Expectations
Gateway 3

Usability

26/27
0
17
24
27
Usability (Gateway 3)
Meets Expectations
Overview of Gateway 1

Focus & Coherence

The materials reviewed for STEMscopes Math Grade 6 meet expectations for focus and coherence. For focus, the materials assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards. For coherence, the materials are coherent and consistent with the CCSSM.

Criterion 1.1: Focus

06/06

Materials assess grade-level content and give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for STEMscopes Math Grade 6 meet expectations for focus as they assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Indicator 1A
02/02

Materials assess the grade-level content and, if applicable, content from earlier grades.

The materials reviewed for STEMscopes Math Grade 6 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

The curriculum is divided into 18 Scopes, and each Scope contains a Standards-Based Assessment used to assess what students have learned throughout the Scope. Examples from Standards-Based Assessments include:

  • Scope 2: Integers, Evaluate, Standards-Based Assessment, Question 7, “Coco has $47.15 in her checking account. Part A What does this value tell us? Explain your reasoning by using a positive or negative value. Enter your answer in the box. Part B What does a value of zero mean in this situation? Enter your answer in the box.” (6.NS.5)

  • Scope 8: Algebraic Expressions, Evaluate, Standards-Based Assessment, Question 2, “Juan bought light bulbs and leaf bags from a home improvement store. The expression 0.99b+2.15l0.99b+2.15l represents the total cost. Which statements are true about the expression? Select all that apply. The expression is the sum of the cost of two different items.; The total cost is the product of the terms.; Each coefficient of the terms is greater than 1.; Each term represents the cost of the individual items bought.” (6.EE.2)

  • Scope 10: Ratios, Rates, and Unit Rates, Evaluate, Standards-Based Assessment, Question 3, “Maggie uses 4 cups of water for every 1 cup of distilled vinegar for a cleaning solution. Which statements are true? Select all that apply. For every 8 cups of water, she uses 2 cups of distilled vinegar.; For every 10 cups of water, she uses 3 cups of distilled vinegar.; For every 20 cups of water, she uses 5 cups of distilled vinegar.; For every 26 cups of water, she uses 7 cups of distilled vinegar.; For every 32 cups of water, she uses 8 cups of distilled vinegar.” (6.RP.2)

  • Scope 16: Understand Variability, Evaluate, Standards-Based Assessment, Question 5, “The following questions were asked about houses in a neighborhood. Which of the following are non-statistical questions? Select all that apply. How old is the oldest house on the street?; How many bedrooms does each house on the street have?; How many houses are in the neighborhood?; How many square feet of living space is there in each house?” (6.SP.1)

  • Scope 17: Represent and Interpret Data, Evaluate, Standards-Based Assessment, Question 3, students see a histogram with the label Number of Students on the Y-Axis and the label, Sit-Ups and 0-19, 20-29, 30-39, 40-49, and 50+ along the X-Axis. “The following histogram is supposed to represent the number of sit-ups students completed in two minutes. However, there are two errors in the histogram. Identify these errors. Explain your reasoning. Enter your answer below.”(6.SP.4)

Indicator 1B
04/04

Materials give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for STEMscopes Math Grade 6 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials provide extensive work in Grade 6 as students engage with all CCSSM standards within a consistent daily lesson structure, including Engage, Explore, Explain, Elaborate, and Evaluate. Intervention and Acceleration sections are also included in every lesson. Examples of extensive work to meet the full intent of standards include:

  • Scope 5: Coordinate Plane Problem Solving, Explore, Explore 2–Polygons on a Coordinate Plane, engages students in extensive work to meet the full intent of 6.G.3 (Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.) In Procedure and Facilitation Points, students work in groups to use coordinates to draw polygons. “Part I: Pecan Park East, 1. Read the following scenario to students: Pecan Park received funding to upgrade some of their equipment and facilities. The work is being done in two phases. In Phase 1, Pecan Park East is redesigning the layout of the climber dome, slides, baseball fields, and swings. The park chairperson wants to ensure that none of the equipment or facility areas overlap. Each piece of equipment or facility area is represented by a polygon, and the coordinates of the vertices of each area are given. Plot the coordinates of the vertices, and connect them to mark each area on the coordinate plane to determine whether any areas overlap. 2. Give a Student Journal to each student. 3. Give a set of the Part I: Pecan Park East Cards to each group. 4. Students will work cooperatively to read each card and plot the vertices for each piece of equipment or facility area on the coordinate plane on page 1 of the Student Journal. Once the vertices from each piece of equipment or facility area have been plotted, students will draw a polygon by connecting the points. Students will then use the completed park map to determine whether any of the equipment or facility areas overlap. 5. Monitor student collaboration, and use the following guiding questions to assess understanding: a. DOK–1 What polygon is the climbing dome shaped like? b. DOK–1 How are the coordinates for the slide different from the coordinates of the other equipment or areas? c. DOK–1 How do you plot the coordinate (−2.5, −2.5)? d. DOK–1 Why is it important for these areas to not overlap? Part II: Pecan Park West 1. Read the following scenario to the students: Pecan Park West will hold the basketball court, the sandpit, and the picnic area. Each of these facilities requires additional work to complete the upgrade. Each facility is represented by a polygon, and the coordinates of the vertices are given. Plot the coordinates, and connect them to mark each area on the coordinate plane. Then, help the chairperson determine the additional calculations required to complete the upgrades. 2. Give a set of the Part II: Pecan Park West Cards to each group. 3. Have students work in their groups to plot the vertices for each facility area on the coordinate plane on page 2 of the Student Journal. Once the vertices from each facility area have been plotted, students will draw a polygon by connecting the points. Students will then use the completed park map to determine the additional calculations required to complete the upgrades on the Student Journal. 4. Monitor student collaboration, and use the following guiding questions to assess understanding: a. DOK–1 What is the distance between −5 and −2?   b. DOK–1 Why are there 6 grid boxes on the graph between the coordinates (−5, −2.5) and (−2, −2.5)? c. DOK–1 How do you find the area of a rectangle? d. DOK–1 How do you find the perimeter of a rectangle? e. DOK–1 How do you determine when to calculate the area and when to calculate the perimeter?” Exit Ticket, students continue to use coordinates to determine distance on a coordinate plane. “The sandpit at Pecan Park West is so popular that officials have decided to add one additional sandpit. The vertices of the sandpit have coordinates of (−3, 3), (−5, 3), (−5, 5), and (−3, 5). Determine the number of units of wooden border and weather-proof liner needed to complete the upgrade.”

  • Scope 8: Algebraic Expressions, Explore 1 and 4, engages students in extensive work to meet the full intent of 6.EE.1 (Write and evaluate numerical expressions involving whole-number exponents.) In Explore 1–Writing Expressions, Math Chat and Exit Ticket, students work with a variable to write expressions that represent given situations. In Math Chat (a table is given with the heading: Questions, and another heading: Sample Student Responses), “DOK–1 Group 1 wrote 3x3 \cdot x as their expression, while Group 2 wrote 3(x)3(x). Which group is correct? DOK–1 Why should we not use an x to represent multiplication? DOK–2 How would the expression change if it were the quotient of 3 and x? DOK–1 Are the expressions 13x\frac{1}{3}x and x3\frac{x}{3} equivalent?” Exit Ticket, students complete a table, creating algebraic expressions for given scenarios. “Read each statement. Write the algebraic expression that describes each statement. Statement, Algebraic Expression, 4 times x, 4 decreased by x, the quotient of x and 4, 4 times the difference of 4 and x, 4 plus the product of 4 and x, the product of 2 and x.” In Explore 2-Evaluate Expressions, students work in groups to solve algebraic expressions. “Part I, 1. Post the expressions 232\cdot3 and 2(3)2(3) on the board. Ask the following question: a. DOK–1 Are these expressions equivalent? 2. Post the expressions 2(3)2(3)and 2(x)2(x) on the board. Ask the following question: b. DOK–1 Are these expressions equivalent? 3. Post 2(3)2(3) and "2(x)2(x) when x=3x=3” on the board. Ask the following question: a. DOK–1 Are these expressions equivalent? 4. Explain to students that this is called substitution. Substitution is when you replace a variable in an algebraic expression with a known value. Check for understanding by asking the following questions: a. DOK–1 What is the value of 3(x)3(x) when x=4x=4? 3(4)=123(4)=12 b. DOK–1 What is the value of 5x5x when x=2x=2? 5x5x means 5(x)5(x). 5(2)=105(2)=10 5. Read the following scenario to students: A group of students from South Sydney Middle School went to the National Zoo of Australia on a field trip. The students were split into groups, each chaperoned by an adult. At lunchtime, groups examined the menu and compiled their orders into an algebraic expression, which included a tip of $3. Each group had a $40 limit to spend on lunch. Prior to placing the orders, the chaperones wanted to ensure that each group’s order was under budget. Evaluate the expressions representing each group’s order to determine their total and whether they were under or over their $40 limit. 6. Give a Student Journal to each student and an Outback Snack Shack Menu to each group. 7. Explain to students that they will use the prices on the Outback Snack Shack Menu to evaluate the expressions for each group to determine the total cost of lunch. Remind students of the $40 limit. 8. Allow students to collaborate with their groups to complete Part I of the Student Journal. As they work, ask the following questions: a. DOK–1 How do you know which mathematical operation to perform first? b. DOK–1 What does the variable s represent? c. DOK–1 What is the total cost for Group 5’s order? d. DOK–1 How do you determine what to remove from an order if a group is over the $40 budget? Part II, 1. Read the following scenario to students: Groups 7 and 8 lost their lunch orders, but they know how much they spent in relation to Group 6. They read their verbal descriptions to their chaperones to determine how much each group spent on their lunch orders. 2. Explain to students that they will use the verbal descriptions in Part II on the Student Journal to write algebraic expressions to represent the total spent by each group, and then find the total of all three groups. 3. Upon completion of Part II, have students answer the reflection questions on the Student Journal.” 

  • Scope 10: Ratios, Rates, and Unit Rates, Explore, Explore 1-3 engage students in extensive work to meet the full intent of 6.RP.1 (Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.) In Explore 1 - Ratios, Procedure and Facilitation Points, students use a Fruit Stand Scenario to understand a ratio. “1. Read the following scenario: Trixie is picking fruit from her fruit farm to sell at the local farmers’ market fruit stand. Each week, she picks different fruits, depending on that week’s demand. She wants to keep a log of each week’s demand by representing the numbers of each type of fruit in the form of a ratio. Help her determine the ratio between each type of fruit that she brings to the market each week. 2. Display the Fruit Stand Card for week 1. a.  Discuss the following questions with the students:How many blueberries are there for week 1? There are 6 blueberries. b. How many strawberries are there for week 1? There are 8 strawberries. c.We want to show the relationship of strawberries to blueberries in week 1. (Write out, “There are ___ strawberries for every ___ blueberries.To model the relationship between strawberries and blueberries, what would we need to fill in the blanks with? In the first blank we would need to put 8 because there are 8 strawberries. In the second blank we will need to write 6 because there are 6 blueberries. d. Explain to class: Mathematicians call this relationship a ratio. Mathematicians write ratios in the order that the ratio asks.  In this scenario, we want to represent strawberries to blueberries, therefore we write the number for strawberries in the first spot and the number for blueberries in the second spot. We can also write the ratio for the information shown in week 1’s Fruit Stand Card in the following ways: “For every 8 strawberries, there are 6 blueberries”; “8:6”; “8 to 6”; or “There are 8 strawberries for every 6 blueberries.’ e. How can we draw a tape diagram to represent the relationship between strawberries and blueberries? Draw one tape diagram with 8 spaces to represent the strawberries. Below draw a tape diagram that is only 6 spaces to represent the 6 blueberries.Model for students how to draw the tape diagram model for 8 strawberries to 6 blueberries. f. As you work through each week’s scenario, we will learn other ways to represent ratio relationships as well. 3. Give one Student Journal to each student and one set of Fruit Stand Cards to each group. 4. Students will work collaboratively to represent the information on each Fruit Stand Card. They will record the number of each type of fruit, draw a tape diagram to show the number of each type of fruit, and then write the ratio describing their models in two different ways. 5. Provide linking cubes to students who are struggling. Have students model the ratio with linking cubes by linking the correct amount together for each fruit in the scenario. Then students can draw a model of their linking cubes as a tape diagram on the Student Journal. In Explore 2 - Ratio Tables and Graphs, Procedure and Facilitation Points PART II,  students use ratio language to describe a ratio relationship between two quantities. “1. Read the following scenario: Trixie wants to use the ratios of fruit bushes in her current farm to determine the number of bushes she should plant in the expansion. Using the Purchasing Fruit Bushes Cards – Part II, determine the ratios for each comparison to help Trixie find equivalent ratios of fruit bushes that she could plant at the farm. 2. Give a Purchasing Fruit Bushes Card – Part II to each group. 3. Students will work collaboratively to use the information on the Purchasing Fruit Bushes Cards – Part II to determine the ratio for raspberry bushes to blueberry bushes and the ratio for strawberry bushes to blackberry bushes that Trixie has in her garden. Then they will use these ratios to complete the ratio tables for each comparison and answer the questions that follow on the Student Journal.

  • Scope 11: Percents, engages students in extensive work to meet the full intent of 6.RP.3c (Find a percent of a quantity as a rate per 100…; solve problems involving finding the whole, given a part and the percent.) Explain, Show What You Know - Part 1: Represent Percents Using a 100s Grid, students need to determine the equivalent fractions by using 100s grid. For example, “Solve each problem. Show your work using a 100s grid and/or by determining equivalent fractions. 620\frac{6}{20} of the students walk to school each day. What percent of students walk to school? Workspace with a 100s grid. Solution Statement: ___” Show What You Know - Part 2: Solving Percent Problems Using Benchmark Fractions and Percents, students complete missing information for a given scenario, “Scenario: Vera poured 500 mL of water into her bottle at the start of the day. By noon, she had drunk 25% of the water. How many mL of water had Vera drunk by noon?”

  • Scope 17: Summarize Numerical Data, Explore 1-Mean and Median and Show What you Know-Part 1: Mean and Median, engage students with extensive work to meet the full intent of 6.SP.2 (Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.) Explore 1, Procedure and Facilitation Points, students work in groups to find the center and create dot plots. “Part I: Mean as Balance Point 1, Read the following scenario to the class: José is tracking his total number of home runs and total number of hits for several series of baseball games he has played in. José wants to determine how many home runs and how many total hits he would have to have in each series to have balanced out his hits and home runs evenly between each series. Help José find the mean as a balance point to determine the number of home runs and the number of total hits he would have to have in each series to balance the home runs and total hits. 2. Give a Student Journal to each student. 3.Give a set of José’s Baseball Scenario Cards and linking cubes to each group. 4. Have students discuss what the term balance point means. Explain to students that the balance point is the mean of a data set. 5.Have students use José’s Home Runs scenario card to record the number of home runs hit in each series on the table in the Student Journal. Students will also create a dot plot to represent the number of home runs hit in each series. They will use the linking cubes to represent the data points for José’s home runs. Note: One linking cube represents one data point (table). For example, in series 1 José has 3 home runs = 3 linking cubes. 6. Have students stack the linking cubes to represent each series. Note: Series 1 should have 3 cubes, series 2 should have 1 cube, series 3 should have 5 cubes, series 4 should have 5 cubes, and series 5 should have 1 cube. Once the correct number of linking cubes is stacked for each series, students should figure out how many cubes each series should have to have an equal number of home runs hit by redistributing the stacks so that each stack has an equal amount of cubes. Students will only use cubes for José’s Home Runs scenario card. 7. Actively monitor students as they are working with their groups using the cubes to understand mean as the balance point. Ask questions such as the following: a. DOK–1 How can you use the linking cubes to determine the balance point? b. DOK–2 How do you think the balance point would be affected if we added more data points above the balance point? c. DOK–2 How can you interpret mean as the balance point using a dot plot? 8. Allow time for students to input the data from both of José’s Baseball Scenario Cards and create their dot plots. They will analyze each dot plot by answering questions and then answer the Part I reflection questions. Part II: Finding the Center and Shape of Data 1. Read the following scenario to the class: Sammy wants to track the total number of times he is up to bat and the total number of hits that he has for the past seven series of baseball games he has played in. Sammy will use his data to determine the middle value and the average number of times that he is up to bat as well as the middle value and average number of hits he has per series. Help Sammy find the center and shape of data using the histogram. 2. Give a set of Sammy’s Baseball Scenario Cards to each group. 3. Encourage students to discuss their observations with their groups as they work through Sammy’s Baseball Scenario Cards. 4. Explain to students that they will use Sammy’s Baseball Scenario Cards to record Sammy’s total times at bat and Sammy’s total hits in the frequency tables on the Student Journal. They will use the frequency tables to create histograms. 5. Monitor and assess students as they are working by asking the following questions: a. DOK–2 Why do you have to arrange the numbers from least to greatest? b. DOK–1 How do you find the middle value if there are two middle numbers? c. DOK–1 How can you determine the mean in a data set? d. DOK–1 How can you identify the shape of the data distribution? 6. Ask students, “What other term might you use for the middle value?” Accept all reasonable answers. Inform students that mathematicians call the middle value the median.” On the Exit Ticket, students are given a table of numbers representing the number of hits in recent games. “Jerry recorded the number of hits he has had in his most recent baseball games. Use the information in the table to create a dot plot that shows the number of hits Jerry has had. 30, 31, 33, 33, 34, 34, 34, 35, 35, 35, 35, 35, 36, 36, 36, 36, 37, 37, 38, 40, Title:, 1. Determine the mean of the data set. 2. Determine the median of the data set. 3. What is the shape of the data?

Criterion 1.2: Coherence

08/08

Each grade’s materials are coherent and consistent with the Standards.

The materials reviewed for STEMscopes Math Grade 6 meet expectations for coherence. The materials: address the major clusters of the grade, have supporting content connected to major work, make connections between clusters and domains, and have content from prior and future grades connected to grade-level work.

Indicator 1C
02/02

When implemented as designed, the majority of the materials address the major clusters of each grade.

The materials reviewed for STEMscopes Math Grade 6 meet expectations that, when implemented as designed, the majority of the materials address the major cluster of each grade.

The instructional materials devote at least 65% of instructional time to the major clusters of the grade:

  • The approximate number of scopes devoted to major work of the grade (including assessments and supporting work connected to the major work) is 12 out of 18, approximately 67%.

  • The number of lesson days and review days devoted to major work of the grade (including supporting work connected to the major work) is 118 out of 155, approximately 76%.

  • The number of instructional days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 132 out of 180, approximately 73%.

An instructional day analysis is most representative of the instructional materials because this comprises the total number of lesson days, all assessment days, and review days. As a result, approximately 73% of the instructional materials focus on the major work of the grade.

Indicator 1D
02/02

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The materials reviewed for STEMscopes Math Grade 6 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Materials are designed so supporting standards/clusters are connected to the major standards/ clusters of the grade. Examples of connections include:

  • Scope 7: Equivalent Numerical Expressions Explain, Show What You Know–Part 1: Greatest Common Factors, connects the supporting work of 6.NS.4 (Find the greatest common factor or two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12…) to the major work of 6.EE.3 (Apply the properties of operations to generate equivalent expressions...) and 6.EE.4 (Identify when two expressions are equivalent…) Students use the greatest common factor to generate equivalent expressions. “A florist is making mixed bouquets with roses and carnations. The florist has 36 roses and 48 carnations. Each bouquet must have the same combination of flowers, and all flowers must be used. What is the greatest number of mixed bouquets that the florist can make? A table shows blanks for factors for Roses and Carnations, Common Factors, and Greatest Common Factor. ___ bouquets can be made. ___ roses and ___ carnations in each bouquet.”

  • Scope 8: Algebraic Expressions, Explore, Explore 4–Evaluate Expressions, Exit Ticket, connects the supporting work of 6.NS.3 (Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation) to the major work of 6.EE.2 (Write, read, and evaluate expressions in which letters stand for numbers). Students evaluate expressions given decimal numbers to determine the cost of a meal. “Outback Snack Shack, Exit Ticket, 1. Based on the condensed menu to the right, the following expression was ordered: 5(h+s)+2f+35(h+s)+2f+3 Use substitution to determine the total cost of the order.” Hamburger, h, $4, Salad, s, $4.25, Fries, f, $3, and Apple Slices, a, $3.50.

  • Scope 14: Area and Volume, Explore, Explore 1–Discovering Area Formulas, Exit Ticket, connects the supporting work of 6.G.1 (Find the area of right triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes…) to the major work of 6.EE.3 (Apply the properties of operations to generate equivalent expressions.) Students find the area of a parallelogram by making it into a rectangle and subtracting the area of two triangles. Students provide the formula and then evaluate the expression.  “X-traordinary Landscaping Company is creating a blueprint of the Tranquility Garden and wants to know the area of the garden. Decompose and rearrange the garden figure to create a new garden in the shape of a rectangle. Label the base and the height of each garden. Find the area in square units of both gardens using the area formula. Each grid square is 1 square unit. Tranquility Garden, b = ___ units, h = ___ units, How can you find the area of this garden? Formula: Area:, New Garden, b = ___ units, h = ___ units, How can you find the area of this garden? Formula: Area”

Indicator 1E
02/02

Materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

The materials for STEMscopes Math Grade 6 meet expectations that materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. 

Materials are coherent and consistent with the Standards. These connections are sometimes listed for teachers in one or more of the three sections of the materials: Engage, Explore and Explain. Examples of connections include:

  • Scope 6: Positive Rational Number Operations, Explore, Explore 3–Division of Fractions, Procedure and Facilitation Points connects The Number System domain to the Ratios & Proportional Relationships domain. Students use visual and algebraic representations to show their division of fractions. “1. Read the following scenario to students: Demarcus needs to determine if there will be enough fabric to create tablecloths for the tables at the fundraiser. Model division of fractions using number lines to determine how many tablecloths can be made using each color of fabric. 2. Give one set of Tablecloth Fabric Cards to each group and one Student Journal to each student. 3. Ask the class the following questions: a. DOK-1 How can you model division of fractions using the pattern we discovered in the previous Explore activity? We can multiply the first numerator by the second denominator and then multiply the first denominator by the second numerator. b. Explain new vocabulary to the class: Mathematicians call this the reciprocal or multiplicative inverse. 4. Have students work with their groups to determine the amount of tablecloths that can be made with each color of fabric. Students should start with the blue fabric card before moving on to the remainder of the Tablecloth Fabric Cards.”

  • Scope 9: Equations and Inequalities, Explain, Show What You Know–Part 1: Write, Model, and Solve Equations, connects the major work of 6.EE.A (Apply and extend previous understandings of arithmetic to algebraic expressions) to the major work of 6.EE.B (Reason about and solve one-variable equations and inequalities). Students create a model based on a scenario, then write an algebraic equation and solve it. For example, “Complete the missing information. Scenario: Four candy bars of the same type are lined up end to end and measure 20 inches. What is the length of each candy bar? Model ___; Equation ___; Solution Statement ___”.

  • Scope 10: Ratios, Rates, and Unit Rates, Explain, Show What You Know –Part 3: Rates and Unit Rates, connects the Ratios & Proportional Relationships domain to the Expressions & Equations domain. Students find the unit rate based on the given scenario. For example, “Complete the missing information. Scenario: A train travels at a constant rate. It travels 360 miles in 6 hours. What is the train’s rate of speed per hour? Strategy ___; Unit Rate ___.”

  • Scope 18: Summarize Numerical Data, Explain, Show What You Know–Part 4: Comparing Different Representations of the Same Data, connects the supporting cluster 6.SP.B (Summarize and describe distributions) to the supporting work of 6.SP.A (Developing understanding of statistical variability). Students answer some statistical questions based on the data provided in different graphs within the context. For example, “A convenience store kept track of how many bottles of sunscreen were sold each day. The results are shown on a box plot, a dot plot, and a histogram. Analyze each representation, and answer the questions on the second page. Justify each response by referencing and explaining a specific data representation. Three graphs are provided Graph 1 is a box plot, with min 1 max 8, Q1 at 3, Q2 at 4, and Q3 at 7; Graph 2 is a dot plot, one dot at 1, one dot at 2, 3 dots at 3, 3 dots at 4, 2 dots at 5, 2 dots at 7, and 2 dots at 8; Graph 3 is a histogram, horizontal axis labeled x, step 2, vertical axis labeled y and frequency, the first bar has frequency 2, the 2nd bar has frequency 6, the third bar has a frequency 2, and the fourth bar has frequency 6. Justify each response by referencing and explaining a specific data representation. Question 1: For how many weeks did the convenience store collect the data?; Question 2: What is the approximate center or typical amount of bottles sold each day?; Question 3: What is the median or middle amount of bottles sold?; Question 4: What is the range?; Question 5: Are there any gaps in the data?; Question 6: Between which two values did 50% of all sales fall?”

Indicator 1F
02/02

Content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

The materials reviewed for STEMscopes Math Grade 6 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

Prior and future connections are identified within materials in the Home, Content Support, Background Knowledge, as well as Coming Attractions sections. Information can also be found in the Home, Scope Overview, Teacher Guide, Background Knowledge and Future Expectations sections. 

Examples of connections to future grades include:

  • Scope 2: Integers, Home, Content Support, Coming Attractions, connects 6.NS.C (Apply and extend previous understandings of numbers to the system of rational numbers.) to work in grade 7. “Seventh-grade students extend their understanding of positive and negative numbers to understand subtraction of rational numbers as adding the additive inverse, pq=p+(q)p-q=p+(-q). They will relate the distance between two rational numbers as the absolute value of their difference and apply this principle in real-world contexts.”

  • Scope 7: Equivalent Numerical Expressions, Home, Scope Overview, Teacher Guide, Future Expectations, connects 6.EE.A (Apply and extend previous understandings of arithmetic to algebraic expressions.) with future work in grade 7. “Visual representations and concrete models can help students develop understanding as they move toward using abstract symbolic representations in seventh grade. Students build on their understanding of multiples, factors, and mathematical properties to generate and use the arithmetic of rational numbers.”

  • Scope 16: Understand Variability, Home, Content Support, Coming Attractions, connects 6.SP.1 (Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers…) to the future work. “Students in seventh grade use random sampling to draw inferences about populations, they investigate chance processes, and they develop, use, and evaluate probability models. In eighth grade, students investigate patterns of association in bivariate data. This work extends into high school, where students continue to interpret categorical and quantitative data, and then explore conditional probability and the rules of probability.”

Examples of connections to prior grades include:

  • Scope 4: Coordinate Planes, Home, Content Support, Background Knowledge connects 6.NS.C (Apply and extend previous understandings of numbers to the system of rational numbers.) to work done in previous grades. “In previous grades, students understood positive rational numbers as points on a number line. They have represented real-world and mathematical problems by graphing and interpreting points in the first quadrant of the coordinate plane.”

  • Scope 11: Percents, Home, Scope Overview, Teacher Guide, Background Knowledge, connects 6.RP.3c (Find a percent of a quantity as a rate per 100…; solve problems involving finding the whole, given a part and the percent.) to previous work in grades 4 and 5. “Students are introduced to the concept of rate and multiplicative comparisons beginning in grade four. In fourth grade, students use two-column tables to record conversions between measurements. In Grade 5, students built on multiplicative comparisons to interpret multiplication as scaling and to apply an understanding of fractions as decimals. Fifth-grade students plotted points on the coordinate plane, and they generated and graphed numerical patterns. Prior to this scope, sixth-grade students studied the concept of a ratio as an association between two quantities, and they used ratio language to describe ratio relationships. Tape diagrams, double number lines, tables, and graphs are featured strategies applied when solving mathematical and real-world problems. Experiences with ratio and unit conversion tables provide the foundation for understanding percents, which begins in grade six.” 

  • Scope 13: Dependent and Independent Variables, Home, Scope Overview, Teacher Guide, Background Knowledge connects 6.EE.C (Represent and analyze quantitative relationships between dependent and independent variables.) to work prior to the 6th grade. “In previous grades, students have generated numerical patterns involving positive rational numbers. Students generated two corresponding numerical patterns and analyzed the relationship between them using an input/output table and by graphing the corresponding ordered pairs on the coordinate plane."

Indicator 1G
Read

In order to foster coherence between grades, materials can be completed within a regular school year with little to no modification.

The materials reviewed for STEMscopes Math Grade 6 foster coherence between grades and can be completed within a regular school year with little to no modification. 

According to the STEMscopes Grade 6 Scope List, there are 18 Scopes, each with between 1 and 6 Explores. In addition, there are materials for Daily Numeracy and Mathematical Fluency. According to the Teacher Toolbox, Parent Letter, lessons are built by using the research-based 5E+IA model, which stands for Engage, Explore, Explain, Elaborate, Evaluate, Intervention, and Acceleration. The Engage section includes Accessing Prior Knowledge, Foundation Builder, and Hook. With the Explores, there are Virtual Manipulatives and Skill Basics. The Explain Section includes Anchor Charts, Picture Vocabulary, Interactive Vocabulary, Show What You Know, and Interactive Notebook. The Elaborate section includes Fluency Builder, Spiraled Review, PhET (Interactive Simulations), and Data Science. The Evaluate section includes Standards Based Assessment, Mathematical Modeling Task, Technology-Enhanced Questions, and Skills Quiz. The Intervention and Acceleration sections include Skill Review and Practice, Quick Check, Review, Checkup, Interactive Skill Review, Supplemental Aids, Would You Rather, and Choice Board.

STEMScopes provides a Scope and Sequence for each grade level, “The STEMscopes Math Suggested Scope and Sequence for each grade level is based on a 180-day school calendar. The natural progression of mathematics was the greatest factor in determining the order of scopes.” The Scope and Sequence assigns All Weeks to Daily Numeracy and Mathematical Fluency.

The STEMscopes Math Suggested Scope and Sequence for Grade 6 provides each scope, name, and number of weeks to be spent on the scope. “STEMscopes Math Suggested Scope and Sequence, The STEMscopes Math program is flexible, and there are variations in implementation within the guidelines provided here. This Scope and Sequence is meant to serve as a tool for you to lean on as you find how STEMscopes Math best meets the needs of the students in your classroom.”

StemSCOPES provides several choices for the Grade 6-8 Lesson Planning Guide, which includes activities from the Engage, Explore, Explain, Elaborate, Intervention, and Acceleration sections, and Assessment and Closure which includes Exit Ticket, Show-What You Know, and Standards Based Assessment. Teachers may choose a Lesson Planning Guide for class length (50 minutes or 90 minutes), instruction structure (whole group or small group), and number of Explores (1-3 Explores or 3-6 Explores). Footnotes on the Lesson Planning Guide advise teachers: “The essential elements are highlighted. If time is limited, teach these elements to fully cover the standards. ¹Use (Foundation Builder) as intervention if APK shows foundational gaps. ²Set your pace according to the number of Explores included in this scope. Use Exit Tickets as well as Show What You Know for each Explore completed. ³Choose from the following elements. (Teacher Choice³ Meets level: Would You Rather, Choice Board, Approaching Level: Interactive Practice, Skills Quiz) We have suggested activities for students including recommended tasks for students at each skill level.”

In Grade 6, the STEMscopes Math Suggested Scope and Sequence shows 180 days of instruction including:

  • 142 lesson days

  • 17 scope assessment days

  • 13 review days

  • 3 days for Pre, Mid, and Post-Assessment

  • 5 days for State Testing

Overview of Gateway 2

Rigor & the Mathematical Practices

The materials reviewed for STEMscopes Math Grade 6 meet expectations for rigor and balance and practice-content connections. The materials help students develop procedural skills, fluency, and application. The materials also make meaningful connections between the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

Criterion 2.1: Rigor and Balance

08/08

Materials reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications.

The materials reviewed for STEMscopes Math Grade 6 meet expectations for rigor. The materials develop conceptual understanding of key mathematical concepts, give attention throughout the year to procedural skill and fluency, and spend sufficient time working with engaging applications of mathematics. There is a balance of the three aspects of rigor within the grade.

Indicator 2A
02/02

Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The materials reviewed for STEMscopes Math Grade 6 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

STEMscopes materials develop conceptual understanding throughout the grade level. In the Teacher Toolbox, STEMscopes Math Philosophy, Elementary, Conceptual Understanding and Number Sense, STEMscopes Math Elements, this is demonstrated. “In order to reason mathematically, students must understand why different representations and processes work.” Examples include:

  • Scope 6: Positive Rational Number Operations, Explore, Explore 2–Modeling Fraction Division, Procedure and Facilitation Points, students develop conceptual understanding as they model fraction division. “1. Read the following scenario to students: Each of the grade levels at Sally’s school will be in charge of some part of the fundraiser. Sally’s grade level is in charge of partitioning baked goods into individual packages to be sold at the dessert booth. The sixth-grade teachers prepared Fundraiser Dessert Cards with instructions on how each dessert should be partitioned. Determine how many individual packages of each dessert item can be made with the information provided on the Fundraiser Dessert Cards. 2. Assign each group a station at which to begin working. 3. Give a Student Journal to each student. 4. Students will read the information on each Fundraiser Dessert Card at their stations. 5. Have students discuss in their groups what they could do to find how many individual packages can be made with the total amount of dessert. a. Students should determine that they can divide the total amount of dessert into fractional pieces based on the information that is provided to them. 6. Encourage students to use the provided Cuisenaire Rods to build a concrete model to solve. 7. As students work, move from group to group and scaffold as needed. Remind students to draw a pictorial model of the concrete model, write a solution equation, and write a solution statement in the Student Journal. Optionally, have students use their colored pencils to show each different-colored rod that was used. a. Students may struggle to determine which pieces to use for each part. Guide students to using the following rods: i. Station 1– Use the blue rod to equal one whole. ii. Station 2–Use the light green rods to model eighths. iii. Station 3–Use the dark green rod to equal one whole. 8. Monitor and assess students’ understanding as they collaborate by asking the following guiding questions: a. DOK-1 How can you partition the chocolate cake into thirds? b. DOK-1 What do you do with extra Cuisenaire Rods if you do not have one whole? c. DOK-1 Can you use a fraction in the quotient? 9. Have students rotate to the remaining stations, continue to build concrete models to solve, and record their thinking on their Student Journals.” (6.NS.1)

  • Scope 7: Equivalent Numerical Expressions, Explore, Explore 2–Prime Factorization, students develop conceptual understanding about factors, prime number, composite number, and prime factors. An example is “Part I, Display the Factor Tree Discussion Card for students. Give a Student Journal to each student. Discuss the following concepts and questions with the class: Look at the diagram shown on the board. DOK-1 What are two factors that will result in 120? DOK-1 What is a prime number? DOK-1 What is a composite number? DOK-1 Are twelve and ten prime numbers or composite numbers? DOK-1 Can twelve and ten be decomposed into more factors? DOK-1 What are two factors of 12? DOK-1 Are either of the factors six or two prime numbers? DOK-1 Should we continue to decompose prime numbers like two? Prime numbers can only be decomposed into one and itself. Therefore, once we reach a prime number, we do not need to decompose that factor again. Explain to students that once we get a prime number, we will circle it so we know that we do not need to continue to find factors for that number. DOK-1 What are two factors of 10? DOK-1 Are either of the factors two or five prime numbers? DOK-1 What are two factors of 6? DOK-1 Are either of these factors prime? DOK-1 What do you notice about the factors that are circled? DOK-1 How can you write these prime numbers as an expression? Explain to class: Mathematicians call this expression the prime factorization. Mathematicians write prime factorization expressions from least to greatest. … Give one Factor Tree Diagram Card and one dry-erase marker to each group. Discuss the following items with the class: Think about what the prime factorization expression would be if we started the factor tree with different factors than twelve and ten. DOK-1 What are two other factors of 120? Discuss the following question with the class: DOK-1 Is the prime factorization expression for this factor tree the same or different than the first one? Explain.” (6.NS.4)

  • Scope 10: Ratios, Rates, and Unit Rates, Engage, Hook, Procedure and Facilitation Points, students develop conceptual understanding of ratios and use proper terminology. “Part I: Pre-Explore, 1. Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. 2. Explain the situation while showing the video behind you. Mr. Smith is everyone’s favorite custodian at Lincoln Middle School. Every few weeks he gets out his ladder and climbs on top of the school roof to collect the balls that have gotten stuck up there during PE, recess, and post-lunch games and sports. Mr. Smith has decided to evaluate the data he collected to determine which balls get stuck most often. Once he knows, he will put the data in the form of a ratio, demonstrating which type of ball makes up the biggest share of total balls stuck on the roof. Then, he will recommend that students play sports and games that use those balls farther from the school building at locations such as the field or track. 3. Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? Allow students to share all ideas. Student answers will vary. I notice that Mr. Smith is using ratios. I wonder what balls will be found on the roof. What ball will Mr. Smith find to be most common on the roof? How many total balls will be found on the roof? I can use math to compare quantities of balls found on the roof in the form of ratios. 4. Project He’s a Baller! 5. Explain to students that Mr. Smith found 12 balls on the roof. The types of balls include soccer balls, footballs, and tennis balls. Each type of ball was found in a different quantity. a. DOK-1 What is a ratio? b. DOK-2 What ratios could be created from the balls visible on the slide? c. DOK-1 How many balls were found in all? d. DOK-1 How many of each type of ball were found?” (6.RP.1)

The materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade level. Examples include:

  • Scope 2: Integers, Explain, Show What You Know–Part 1: A Number and Its Opposite, Student Handout, students plot numbers on a number line. “Locate and plot the integers that are 2 units above and 2 units below zero.” Students see a vertical number line with a 0 in the middle and tick marks above and below.  To the right of the number line, there is a box for students to write the positive integer and the negative integer that they have just plotted.  Below those boxes are two more boxes with the title “What is the distance of each integer from zero?” (6.NS.5)

  • Scope 7: Equivalent Numerical Expressions, Explain, Show What You Know–Part 2: Prime Factorization, students work to understand the concept of factor tree and prime factorization. An example is “Complete the missing information. Number18, Factor Tree ___; Prime Factorization ___; Number100, Factor Tree ___; Prime Factorization ___.” (6.NS.4)

  • Scope 8: Algebraic Expressions, Elaborate, Fluency Builder-Match Equivalent Algebraic Expressions, Procedure and Facilitation Points and Instruction Sheet, students solve algebraic expressions as well as finding equivalent expressions. Procedure and Facilitation Points example is  “1. Show students how to shuffle the cards and place them face down in a 4×64\times6 array. 2. Model how to play the game with a student. a. Player 1 flips over 2 cards to try to find a match. A match is a problem with its correct answer. Problems will need to be solved in order to determine matching answers. b. If player 1 matches a problem with the correct answer, then player 1 keeps the matched set and takes another turn. c. If player 1 does not find a match, then they place the cards face down again, and it is the next player’s turn. d. Players continue taking turns until all of the matches have been found. e. The player who collects the most cards wins. 3. Distribute materials. Then, instruct students to shuffle the cards and lay them facedown. 4. Monitor students to make sure they find accurate matches.” The Concentration Cards have algebraic expressions with a matching pair for each.  Instruction Sheet, “Concentration Instruction Sheet Play this game with a partner. You Will Need 1 Set of Concentration Cards (per pair) How to Play 1. Shuffle the cards, and place them face down to form a 4 × 6 array. Player 1 flips over two cards to try to find a match. A match is a problem with its correct answer. Problems will need to be solved in order to determine matching answers. 3. If player 1 matches a problem with the correct answer, then player 1 keeps the matched set and takes another turn. 4. If player 1 does not find a match, then they place the cards face down again, and it is the next player's turn. 5. Players continue taking turns until all of the matches have been found. 6. The player who collects the most cards wins.” (6.EE.4)

Indicator 2B
02/02

Materials give attention throughout the year to individual standards that set an expectation for procedural skill and fluency.

The materials reviewed for STEMscopes Math Grade 6 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

STEMscopes materials develop procedural skills and fluency throughout the grade level. In the Teacher Toolbox, STEMscopes Math Philosophy, Elementary, Computational Fluency, STEMscopes Math Elements, these are demonstrated.  “In each practice opportunity, students have the flexibility to use different processes and strategies to reach a solution. Students will develop fluency as they become more efficient and accurate in solving problems.” Examples include:

  • Scope 2: Integers, Elaborate, Fluency Builder–Integers, students develop procedural skill and fluency, with teacher support, understanding that positive and negative numbers are used together to describe quantities. “Procedure and Facilitation PointsShow students how to shuffle the cards. Model how to play the game with a student. Pass out five cards to each player. Place the rest of the deck in a pile on the table. Players take turns asking each other for either the answer to match one of the problem cards or the problem card to match one of the answer cards. If the opponent has the matching card, the opponent must give it to the player. If the opponent does not have the matching card, the other player must pick a card from the deck.The winner is the player with the most matches when all of the cards are gone.Monitor students to make sure they find accurate matches.” (6.NS.5)

  • Scope 6: Positive Rational Number Operations, Elaborate, Fluency Builder–Multiply and Divide Decimals, students develop procedural skill and fluency of multiplying and dividing decimals, with teacher support.  “Procedure and Facilitation PointsShow students how to fold the cards and place them in the jar. Model how to play the game with a student. Player 1 pulls out a card from the jar and hands it to player 2. Player 2 will read the question aloud for player 1 to solve. Player 2 can check the answer from player 1 at the bottom of the card. If a player gets a problem correct, they keep the card. If they are incorrect, the other player keeps the card. Note: If the card contains an image such as a graph or a number line, the player asking the question can show the image while covering up the answer with their hand.If a player pulls out a Bam! picture card, all of that player’s cards go back into the jar. Players take turns pulling cards from the jar and answering questions until time is up. Players must try to get as many cards as they can before time is up. The player with the most cards wins. Set a time limit. When time is up, the student with the most cards wins.  Distribute materials, and instruct students to begin when the timer starts. Monitor students to make sure they solve problems correctly.” (6.NS.3)

  • Scope 7: Equivalent Numerical Expressions, Explore, Explore 1–Exponents, Procedure and Facilitation Points, Part 1, students develop procedural skill by rewriting expressions using exponents. “1. Read the following scenario: BEST Party Planners are ready to turn in their order forms for cupcakes to their boss. Their boss has asked them to write each order as an exponential expression. Use the information on the Cupcake Order Form to write the prime factorization expression as the order’s expanded form and then rewrite it as an exponential expression to turn into the boss. 2. Give one copy of the Student Journal to each student. 3. Project the Cupcake Order Form for the class. Model simplifying expressions using exponents with students. Discuss the following items with the class: a. BEST Party Planners needs to order two red velvet cupcakes. b. DOK-2 What is the prime factorization of 2? c. DOK-1 How many twos are in this prime factorization expression? d. BEST Party Planners needs to order 4 fudge cupcakes. e. DOK-2 What is the prime factorization of 4? f. DOK-1 How many twos are in this prime factorization expression? h. DOK-2 What is the prime factorization of 8? i. DOK-1 How many twos are in this prime factorization expression? j. DOK-2 What do you notice about the number of twos that are in the prime factorization expression each time? 4. Allow students time to complete the second and third columns for the last three cupcake types. 5. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-1 What is the prime factorization of 32? b. DOK-1 How many twos are in this prime factorization? 6. Discuss the following questions with the class: a. DOK-2 What number is used in every prime factorization? b. Each number of cupcakes was decomposed into an expression involving some number of 2s. DOK-1 For the confetti cupcakes, how many twos need to be multiplied together to get 8? c. Explain to class: Mathematicians call the number that we are repeatedly multiplying together the base. d. We write the base 2 in our cupcakes example in the last column. Model for students writing a 2 in the last column for the confetti cupcakes. e. Look at the confetti cupcakes row again. DOK-1 How many twos are in the prime factorization expression? f. Write a smaller 3 at the top right side of the base 2. Model for students writing the exponent. g. Explain to class: Mathematicians call this smaller number on the top right the exponent or power. h. DOK-1 How many twos are multiplied together in the prime factorization expression for 2? i. DOK-2 What will be the base for red velvet cupcakes? j. DOK-2 What will be the exponent for red velvet cupcakes? 7. Allow students time to work with their partners to write the exponential expression for each of the remaining cupcake orders on the Student Journal. 8. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK-1 How many twos are in the prime factorization expression for strawberry cupcakes? b. DOK-1 What is the exponent for vanilla cupcakes?” (6.EE.1)

The materials provide opportunities for students to independently demonstrate procedural skills and fluency throughout the grade level. Examples include:

  • Scope 2: Integers, Elaborate, Fluency Builder–Integers, Instruction Sheet, students independently demonstrate procedural skill and fluency as they match problem cards to answer cards involving integers. “4. Players take turns asking each other for either the answer to match one of the problem cards or the problem card to match one of the answer cards. If the opponent has the matching card, the opponent must give it to the player. If the opponent does not have the matching card, the other player must pick a card from the deck.” Go Fish! Card example, “Write the integer to represent borrowed $20.” Answer, “-$20.” (6.NS.5)

  • Scope 6: Positive Rational Number Operations, Explain, Show What You Know - Part 1: Divide Multi-Digit Numbers, Student Handout, Questions 1-3, students demonstrate procedural skill and fluency by dividing multi-digit rational numbers. “Each batch of cotton candy uses 12 cups of sugar. How many batches can be made from 1,488 cups of sugar?” (6.NS.2)

  • Scope 10: Ratios, Rates, and Unit Rates, Elaborate, Fluency Builder–Ratios and Rates in Various Representations, students demonstrate fluency by finding unit rates in a card game. One card says, “6 teachers to 15 students on a field trip.” The matching card says, “2.5 students per teacher.” (6.RP.3b)

Indicator 2C
02/02

Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.

The materials reviewed for STEMscopes Math Grade 6 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of mathematics.

STEMscopes materials include multiple routine and non-routine applications of mathematics throughout the grade level, both with teacher support and independently. Within the Teacher Toolbox, under STEMscopes Math Philosophy, Elementary, Computational Fluency, Research Summaries and Excerpt, it states, “One of the major issues within mathematics classrooms is the disconnect between performing procedural skills and knowing when to use them in everyday situations. Students should develop a deeper understanding of mathematics in order to reason through a situation, collect the necessary information, and use the mechanics of math to develop a reasonable answer. Providing multiple experiences within real-world contexts can help students see when certain skills are useful.” 

Engaging routine applications of mathematics include:

  • Scope 5: Positive Rational Number Operations, Engage, Hook, Procedure and Facilitation Points, Part II: Post-Explore, students develop application of dividing fractions. “1. Show the Phenomena Video again, and restate the problem. 2. Refer to That Takes the Cake! and discuss the following questions: a. DOK-1 How can you determine the number of pieces of cake that Stephan will have if he cuts each cake into tenths? b. DOK-1 What model can help you solve this problem? c. DOK-1 What is the equation to find how many pieces of cake Stephan will have if he divides the cakes into tenths? d. DOK-1 If Stephan divides 1121\frac{1}{2} cakes into pieces 110\frac{1}{10} the size of a cake, will he have enough pieces to serve 13 people?” (6.NS.1) 

  • Scope 8: Equations and Inequalities, Explain, Show What You Know–Part 2: Write and Solve Equations, Student Handout, students show application of writing and solving equations through routine problems. “Roberta earns $60 for working 4 hours. What is her hourly rate?” (6.EE.7)

  • Scope14: Volume and Area, Engage, Hook, Procedure and Facilitation Points, students develop application of area and volume formulas with teacher support. “Part II: Post-Explore, 1. Show the Phenomena Video again, and restate the problem. 2. Refer to the Garden Plots slide, and discuss the following questions: a. DOK-1 How can you determine the area of the unique garden? b. DOK-1 What is the area of the unique garden? c. DOK-1 How can you determine the volume of the planter box? d. DOK-1 What is the volume of the planter box?” (6.G.1)

Engaging non-routine applications of mathematics include:

  • Scope 2: Compare and Order Rational Numbers, Explain, Show What You Know–Part 1: Compare Rational Numbers, this activity provides an opportunity for students to independently demonstrate application by putting numbers on the number line and writing inequalities to compare numbers. “The following temperatures were recorded last February in Boston, Massachusetts. Day 1: 0°0\degreeC Day 2: 215°-2\frac{1}{5}\degreeC Day 3: =1.5°=1.5\degree Day 4: 1310°1\frac{3}{10}\degreeC Day 5: 2.2°2.2\degreeC; Question 1: Plot each temperature on the number line. Given a number line; Question 2: Write an inequality to compare the temperatures on days 3 and 4. ___; Question 3: A temperature of 0℃ or below allows water to freeze. On which days did water reach the freezing point? ___; Question 4: Between which two consecutive days was the temperature change the greatest? Justify your reasoning in relation to the number line. ___. ” (6.NS.6c)

  • Scope 12: Measurement Conversions, Evaluate, Mathematical Modeling Task–Time for a Vacation, Student Handout, students demonstrate application of ratio reasoning to convert unit measurements with teacher support. “Time for a Vacation! Summer break is here, and your family is taking you on a camping trip with your friends. The trip will be one week long. Your parents have given you a planning guide so the trip can be exactly how you want. It will be a road trip, so you need to make sure to pack all of your necessities. You should also know how many people will be coming on the trip. Part I: Destination Your family and friends live in San Diego, CA, and have decided to go camping at a campsite. Choose your destination below: Austin, TX: Your map shows that you and your family would travel 2,108 kilometers to reach your destination. Phoenix, AZ: Your map shows that you and your family would travel 571.3 kilometers to reach your destination. Los Angeles, CA: Your map shows that you and your family would travel 180 kilometers to reach your destination. Destination: ___, Distance in Meters: ___, Part II: Water Next, you need to pack water. Each person needs to drink 64 fluid ounces of water each day. Your family will be buying gallon jugs of water to supply everyone with enough to drink. Make sure enough water is packed for everybody on the trip. 1. How many people are going on the trip? 2. How many total fluid ounces do you need for one day? 3. How many gallons do you need for one day? 4. What is the total number of gallons needed? Part III: Camping Gear The final items you need to pack are the tents and sleeping bags. Fill in the quantity and the total weight in ounces in the table below: Item, Weight, Quantity, Total Weight in Ounces, Tent, 3lb., Sleeping Bag, 2lb., What process was used to perform the measurement conversion for your destination, water, and camping gear? How did the quantity impact your total amounts? Justify your answer.” (6.RP.3d)

  • Scope 13: Dependent and Independent Variables, Evaluation, Mathematical Modeling Task– Settling on the Moon, Student Handout, students independently show application of representing and analyzing quantitative relationships between dependent and independent variables. “The time has finally come to establish a human colony on the Moon, and your team will help plan the first one! Part I: Homes You anticipate fast growth in this moon colony, so you will build many homes as you invite families. Each home will cost 2 million dollars. Represent the cost of building homes with a table, a graph, and an equation. Part II: Transportation Settlers will get around town both on moon bikes and in moon mobiles. You and your team will need to design a moon bike that costs $8,000 and a moon mobile that costs $9,000. Both modes of transportation need to be designed for the terrain of the Moon. The settlers will need enough moon bikes and moon mobiles for each family. Select one of your choice to represent with a table, a graph, and an equation. Part III: Food Settlers will spend 1 thousand dollars a month on food. Each family will need to purchase meal plans that will include the nutrition that they will need to survive on the Moon. Represent the cost of meal plans with a table, graph, and equation.” (6.EE.9)

Indicator 2D
02/02

The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.

The materials reviewed for STEMscopes Math Grade 6 meet expectations in that the three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.

All three aspects of rigor are present independently throughout the grade. Examples where instructional materials attend to conceptual understanding, procedural skill and fluency, and application include:

  • Mathematical Fluency: Operations with Integers, Activities, Mathematical Fluency–Different Signs-Activity 1, Procedure and Facilitation Points, students demonstrate procedural fluency to solve problems using the four operations with integers. Students use a fraction puzzle. Each problem has a solution match the student needs to find. “1. Have students work together to cut out all of the triangle puzzle pieces and arrange them faceup on the table. 2. Have students work together to solve expressions and find a matched solution. 3. Each expression is matched with a solution on a different puzzle piece. When a match is found, the triangles are arranged so that the matched expression is opposite and upside down from its solution. 4. Some pieces may share the same solution, but a match is only formed if all 3 sides of each piece correspond to the adjacent sides. 5. When both students agree that all of the pieces have been matched, have students tape or glue the pieces onto the blank paper. Students should glue each piece separately to ensure proper orientation and alignment. 6. Monitor students as they work to ensure that they are following instructions, and assist with computation as needed. 7. Refer to the answer key to check student answers.” (6.NS.5)

  • Scope 2: Integers, Evaluate, Skills Quiz, students demonstrate conceptual understanding using positive and negative numbers to represent quantities in real-world contexts. “Question 1: A diver can swim up to 130 feet below sea level. Write a negative integer to represent the depth that a diver could possibly dive and explain your reasoning. ____.” (6.NS.5)

  • Scope 8: Equations and Inequalities, Explore, Explore 2–Write and Solve Equation, students demonstrate application as students write and solve equations using properties to find the value of the variable. “Procedure and Facilitation Points Read the following scenario: The local amusement park offers parking and pizza deals every Tuesday through Friday. Montrell’s family wants to see which day has the best deals for parking and pizza. Help Montrell’s family determine which day has the better deal by writing and solving equations.If needed, revisit the following Math Chat discussion questions from Explore 1 to review using inverse operations to solve equations. DOK-2 For any multiplication equation, px=qpx=q, how can you find the value of x? DOK-2 For any addition equation, x+p=qx+p=q, how can you find the value of x? … Project Tuesday’s parking price scenario for the class to see. Have a class discussion about using fractions and decimals in equations. Model writing and solving equations with students as you ask the class the following questions: DOK-1 How can I write an equation to represent the price of parking for Tuesday? DOK-1 How can I get the variable h by itself? DOK-1 Does it matter which order I write the division equation on the other side of the equal sign? DOK-1 How do you solve 5÷145\div\frac{1}{4}.  4. DOK-1 What is the price for one hour of parking? DOK-1 How can I write an equation to represent the price for pizza on Tuesday? DOK-1 What step should we take to get the variable p by itself? DOK-1 Does it matter which order I write the subtraction equation on the other side of the equal sign? DOK-1 What is 15.422.1515.42-2.15? DOK-1 What is the price for the pizza on Tuesday? Give a set of Daily Deals Cards to each group. Students will work collaboratively to write and solve an equation for each of the remaining daily deals. As students are working together, monitor their learning, and ask the following questions to check for understanding: DOK-1 What operation do you use to solve the parking price deals? DOK-1 What operation do you use to solve the pizza price deals? DOK-2 What process would you use when your coefficient is a fraction to get the variable by itself? …” (6.EE.7)

Multiple aspects of rigor are engaged simultaneously throughout the materials in order to develop students’ mathematical understanding of a single unit of study or topic. Examples include:

  • Scope 2: Integers, Explain, Show What You Know–Part 1: A Number and Its Opposite, Student Handout, students show conceptual understanding alongside application of knowledge of number lines as they plot numbers on a number line. “Locate and plot the integers that are 2 units above and 2 units below zero.” Students see a vertical number line with a 0 in the middle and tick marks above and below. To the right of the number line, there is a box for students to write the positive integer and the negative integer that they have just plotted. Below those boxes are two more boxes with the title “What is the distance of each integer from zero?” (6.NS.5)

  • Scope 3: Compare and Order Rational Numbers, Evaluate, Skills Quiz, Question 1,  students demonstrate application of rational number knowledge alongside procedural skills by ordering rational numbers. “Question 1:  Order the following rational numbers from least to greatest: - 4,25, -3.5, -2.5, -2.0, -2.75, 3.5, ___, ___, ___, ___, ___, ___.” (6.NS.6c)

  • Scope 6: Positive Rational Number Operations, Explain, Show What You Know–Part 3: Division of Fractions, Student Handout, students demonstrate application of division of fraction skills alongside procedural fluency of dividing fractions. “Complete the missing information. There are 3123\frac{1}{2} sandwiches that are cut into fourths and placed on a platter. How many pieces are on the platter? Divide sandwiches into groups of ___. Equation: Strategy: Use a model or multiply by the reciprocal. Solution statement: Complete the missing information. There is 3 feet of string left on a spool. Packages are being tied with string, and each package requires 34\frac{3}{4} of a foot of string. How many packages can be tied?  Divide feet into groups of ___. Equation: Strategy: Use a model or multiply by the reciprocal. Solution statement:” (6.NS.1)

Criterion 2.2: Math Practices

10/10

Materials meaningfully connect the Standards for Mathematical Content and Standards for Mathematical Practice (MPs).

The materials reviewed for STEMscopes Math Grade 6 meet expectations for practice-content connections. The materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

Indicator 2E
02/02

Materials support the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for STEMscopes Math Grade 6 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Students have opportunities to engage with the Math Practices across the year and are identified for teachers within the Standards of Mathematical Practice within the Explore sections of the scopes. MP1 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students make sense of problems and persevere in solving them as they work with the support of the teacher and independently throughout the scopes. Examples include:

  • Scope 4: Coordinate Plane Problem Solving, Explore, Explore 1–Distances Between Points, Standards of Mathematical Practice, “MP.1 Make sense of problems and persevere in solving them: Students reason about lengths of line segments on the coordinate plane and know the solution for length must be positive (using absolute value) in order for the solution to make sense in real-world applications.” Exit Ticket, students determine the location and distance on a coordinate plane that makes sense in a real-world problem. “The Violet Team has joined in on the group showcase for the rectangular egg toss. The locations of three members of the Violet Team are represented by ordered pairs. Vihaan is located at (7, −3), Gabriel is located at (7, −8), and Hanna is located at (10, −3). 1. Where should Jahzara stand to complete the rectangle? ___, 2. Vihaan is tossing the egg to Gabriel. What is the distance between them in units?___”

  • Scope 6: Positive Rational Number Operations, Explore, Explore 2–Modeling Fraction Division, students seek the meaning of a problem and work to find efficient ways to solve it. Students check the reasonableness of their answers and find alternative strategies as needed. Procedure and Facilitation Points, “Read the following scenario to students: Each of the grade levels at Sally’s school will be in charge of some part of the fundraiser. Sally’s grade level is in charge of partitioning baked goods into individual packages to be sold at the dessert booth. The sixth-grade teachers prepared Fundraiser Dessert Cards with instructions on how each dessert should be partitioned. Determine how many individual packages of each dessert item can be made with the information provided on the Fundraiser Dessert Cards. Assign each group a station at which to begin working.Give a Student Journal to each student. Students will read the information on each Fundraiser Dessert Card at their stations.Have students discuss in their groups what they could do to find how many individual packages can be made with the total amount of dessert. Students should determine that they can divide the total amount of dessert into fractional pieces based on the information that is provided to them. Encourage students to use the provided Cuisenaire Rods to build a concrete model to solve. As students work, move from group to group and scaffold as needed. Remind students to draw a pictorial model of the concrete model, write a solution equation, and write a solution statement on the Student Journal. Optionally, have students use their colored pencils to show each different-colored rod that was used.Students may struggle to determine which pieces to use for each part. Guide students to using the following rods: Station 1–Use the blue rod to equal one whole. Station 2–Use the light green rods to model eighths. Station 3–Use the dark green rod to equal one whole. Monitor and assess students’ understanding as they collaborate by asking the following guiding questions: DOK-1 How can you partition the chocolate cake into thirds? DOK-1 What do you do with extra Cuisenaire Rods if you do not have one whole? DOK-1 Can you use a fraction in the quotient?...”

  • Scope 10: Percents, Explore, Explore 1–Represent Percents Using a Hundreds Grid, Standards of Mathematical Practice, “MP.1 Make sense of problems and persevere in solving them: Students interpret models of fractions and decimals to determine the percent shown.” Procedure and Facilitation Points, “Part I: Understanding Percents Using a Hundreds Grid 1. Read the following scenario to the class: David just started a lawn-mowing business. He schedules 100 customers each week in various neighborhoods with some neighborhoods having a higher percentage of lawns to mow than others. David needs your help determining how many lawns he is mowing in each neighborhood. 2. Give the Percent Work Mat, a dry-erase marker, and a set of colored pencils to each group. 3. Explain to students that a percent is a special ratio that means “out of 100.” It is measured by the number of units as compared with 100. A percent is just another way to show a part-to-whole ratio. A percent can be represented as a fraction, decimal, or ratio since all of these represent a part-to-whole. We will be using the hundreds grid on the Percent Work Mat to represent percents. 4. Guide students in representing a fraction and decimal as a percent. Have students represent 14\frac{1}{4} and 0.03 on the Percent Work Mat. 5. Actively monitor and assess students’ understanding as they collaborate with their groups by asking the following questions: a. DOK-2 What percent is equal to the value of one unit in the grid? Explain. b. DOK-2 How did you represent 14\frac{1}{4} on the Percent Work Mat? c. DOK-2 What percent of the hundreds grid was shaded? d. DOK-2 How did you represent 0.03 on the Percent Work Mat? e. DOK-2  What percent of the hundreds grid was shaded? 7. Give a set of Part I Mowing Cards to each group. 8. Explain to the class that they will be working with their groups to read each Mowing Card and will use the information on the card to create a model using a hundreds grid. 9. Encourage students to use the Percent Work Mat to assist them with determining the percent that is represented for each scenario. They will then collaborate with their groups to determine how the percent is written as a part-to-whole ratio in fraction and decimal form. Once they shade their models on the Percent Work Mat, they will show their work by shading the models found on the Student Journal. They will then use their models to complete the corresponding table of information based on the Mowing Card. 10. Instruct students to simplify each fraction into an equivalent fraction, if possible. 11. Actively monitor and assess student understanding as they collaborate with their groups by asking the following questions: a. DOK-1 What percent is being represented in this scenario? b. DOK-2 How can we represent the lawn care company’s percent of lawns mowed using the hundreds grid? c. DOK-2 How can we represent the lawn care companies amount of lawns mowed as a part-to-whole ratio in fraction form? DOK-2 Can you simplify the fraction into an equivalent fraction? Explain. d. DOK-2 How can we represent the percent of lawns mowed as a part-to-whole ratio in decimal form? …”

MP2 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students reason abstractly and quantitatively as they work with the support of the teacher and independently throughout the scopes. Examples include:

  • Scope 2: Integers, Explore, Explore 1–A Number and Its Opposite, students represent a wide variety of real-world contexts to understand the values of positive and negative rational numbers. Procedure and Facilitation Points, “Read the following scenario to the class: You and your group work for the Top-Notch Rock Wall Company. It’s the top rock wall designers and creators in the country. They have hired your group to assemble different parts of multiple rock wall designs based on customer instructions. It is important to get the placement of each rock wall stone in the correct spot so that these designs accurately match the customers’ requests. Give a Student Journal to each student. Give the Horizontal and Vertical Number Lines, Rock Wall Scenario Cards, and a dry-erase marker to each group. Have students quickly analyze the number lines, and ask the following questions: DOK-1 What is the starting point or middle point on each number line? DOK-1 What is the greatest number for each number line? DOK-1 What is the smallest number for each number line? DOK-1 On a vertical number line, do the numbers increase or decrease as you move farther above zero? DOK-1 On a vertical number line, do the numbers increase or decrease as you move farther below zero? DOK-1 On a horizontal number line, do the numbers increase or decrease as you move to the right of the zero?DOK-1 On a horizontal number line, do the numbers increase or decrease as you move to the left of zero? Explain to students that they will be working with their groups to read each Rock Wall Scenario Card to determine the positive and negative numbers where the rock wall stones will be placed. Mathematicians call positive and negative whole numbers integers.Instruct students to use the number lines to represent their integers. Monitor and assess students as they collaborate by asking the following guiding questions: DOK-2 How can you determine the location of ___ (6 feet above 0, 3 feet to the left of 0, etc.) on the number line? DOK-2 How can you use that location to determine the opposite location? DOK-1 What location do you always start at in order to determine the correct numbers on the number line? DOK-1 What do you notice about the two points on the number line? DOK-3 How would you describe a positive integer? DOK-3 How would you describe a negative integer? A negative integer has a negative symbol in front of it. Allow students enough time to complete all the work for their scenario cards. Explain the following concepts to the class: The numbers you were working with today are known as integers. An integer is any whole number that is positive or negative, including zero. A negative integer is any whole number to the left of zero or less than zero and includes a negative sign in front of the number to represent that it is negative. A positive integer is any whole number to the right of zero or greater than zero…” 

  • Scope 11: Measurement Conversions, Explore, Explore 1–One-Step Measurement Conversions, Standards of Mathematical Practice, “MP.2 Reason abstractly and quantitatively: Students conceptualize relative sizes of units in order to reason about unit conversions.” Exit Ticket, students create a model to use ratio reasoning to convert measurements. “The horns of a bull can weigh approximately 720 grams. If 1 gram is equal to 1,000 milligrams, how many milligrams will the bull’s horns weigh? Model: ___ Equivalent Measurement: ___”

  • Scope 15: Understand Variability, Explore, Explore 1–Variability in Data, Standards of Mathematical Practice, Exit Ticket, Standards of Mathematical Practice, “MP.2 Reason abstractly and quantitatively: Students determine whether a question will have a response with various data or a single data response.” Exit Ticket, students must use reason to determine if a question will have multiple responses. “Survey Tiger was collecting data from a local library. They asked the head librarian the following survey questions. Circle whether the survey questions are statistical questions or non-statistical questions, and explain your response.

Indicator 2F
02/02

Materials support the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for STEMscopes Math Grade 6 meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials provide opportunities for student engagement with MP3 that are both connected to the mathematical content of the grade level and fully developed across the grade level. Mathematical practices are identified for teachers within the Standards of Mathematical Practice within the Explore sections of the Scopes. Students construct viable arguments and critique the reasoning of others, in connection to grade-level content, as they work with support of the teacher and independently throughout the Scopes. Examples include:

  • Mathematical Fluency: Operations with Integers, Dividing, Mathematical Fluency–Different Signs-Activity 1, Procedure and Facilitation Points, students build experience with MP3 as they justify their reasoning for domino placement in a game working on operations with integers. “Model playing the game with a student according to the rules outlined below. a. Players place the dominoes facedown and mix them up. b. Each player chooses three dominoes from the pile and holds them in their hand. c. The extra three dominoes remain facedown. d. The first player places one domino from their hand faceup in the middle of the table. e. The second player chooses a domino with an expression or fraction equal to one side, and places the match together, either in line with the first domino or perpendicular to it. Dominoes cannot be placed side by side. The player must justify their reasoning. If there is an error, and the dominoes are not a match, the player must pick their domino back up and will not get to place another domino until the next turn. f. If a player does not have a matching domino, the player chooses a domino from the extra set and may play that domino if it matches. If it does not match, the player adds the domino to their hand. If there are no more extra dominoes to choose from, the player passes. g. If a match has been made, the player pauses to record the match on the Student Recording Sheet. Players only record their own matches. h. Players continue playing until one person runs out of dominoes, all of the dominoes are used, or they run out of time. i. When the game is over, the student with the most recorded matches wins. 2. Monitor students as they work to ensure that they are following instructions, and assist with computation as needed.”

  • Scope 2: Integers, Evaluate, Mathematical Modeling Task–Stock Values, Part II, students show development of MP3 by justifying how numbers they have chosen meet set criteria. “On Monday, the stock values at Reliable Chemical included numbers based on the following criteria in the table below. Question 1 Input eight possible numbers into the appropriate categories on the table.” Students see a table with three columns. The first column is labeled, “Type of Number.” The second column is labeled “Range.” The third column is labeled “Number.” Students must input numbers in the third column that meet the constraints in the first two columns. “Question 2 Plot each of the numbers on the number line.” Students are provided with a blank number line. “Question 3 Justify how you know that each of the eight numbers meets the criteria from the table.”

  • Procedure and Facilitation Points, students show development of MP3 by performing error analysis on worked problems. “1. Show students how to shuffle the cards and place them face down in a stack. 2. Model how to play the game with a student. a. Shuffle the cards, and place them face down in a stack between the players. b. Player 1 flips over one card. Both players analyze the problem and determine if the provided solution to the problem is correct and the student who answered it is a math expert or if the solution is incorrect and it is necessary to fix the mistake. c. Players take turns flipping over one card at a time. d. Players continue taking turns until all of the cards have been solved. e. Players should fill out the Fix the Mistake! Student Recording Sheet as they play the game. (Players should fill out the row on the Fix the Mistake! Student Recording Sheet that corresponds to each card number.) f. Once all of the cards have been analyzed, students use the Fix the Mistake! Answer Key to check their answers. g. The player with the most correct answers is the winner. 3. Distribute the game materials. Then, instruct students to shuffle the cards and lay them facedown in a stack between the players. 4. Monitor students to make sure they find and record accurate responses to each card using the Fix the Mistake! Student Recording Sheet.” 

  • Scope 11: Measurement Conversions, Evaluate, Mathematical Modeling Task–Time for a Vacation! Part III, students show development of MP3 by explaining the methods they used to convert measurements and justifying their answer. “The final items you need to pack are the tents and sleeping bags. Fill in the quantity and the total weight in ounces in the table below:” Students see a four column table that they will use to determine the quantity and weight of items to take with them. “What process was used to perform the measurement conversion for your destination, water, and camping gear? How did the quantity impact your total amounts? Justify your answer.”

Indicator 2G
02/02

Materials support the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for STEMscopes Math Grade 6 meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Students have opportunities to engage with the Math Practices across the year and are identified for teachers within the Standards of Mathematical Practice within the Explore sections of the Scopes. MP4 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students model with mathematics as they work with the support of the teacher and independently throughout the Scopes. Examples include:

  • Scope 5: Positive Rational Number Operations, Explore, Explore 2–Modeling Fraction Division, Procedure and Facilitation Points, students show development of MP4 as they use Cuisenaire Rods and draw models to represent fraction division. “1. Read the following scenario to students: Each of the grade levels at Sally’s school will be in charge of some part of the fundraiser. Sally’s grade level is in charge of partitioning baked goods into individual packages to be sold at the dessert booth. The sixth-grade teachers prepared Fundraiser Dessert Cards with instructions on how each dessert should be partitioned. Determine how many individual packages of each dessert item can be made with the information provided on the Fundraiser Dessert Cards. 2. Assign each group a station at which to begin working. 3. Give a Student Journal to each student. 4. Students will read the information on each Fundraiser Dessert Card at their stations. 5. Have students discuss in their groups what they could do to find how many individual packages can be made with the total amount of dessert. a. Students should determine that they can divide the total amount of dessert into fractional pieces based on the information that is provided to them. 6. Encourage students to use the provided Cuisenaire Rods to build a concrete model to solve. 7. As students work, move from group to group and scaffold as needed. Remind students to draw a pictorial model of the concrete model, write a solution equation, and write a solution statement in the Student Journal. Optionally, have students use their colored pencils to show each different-colored rod that was used. a. Students may struggle to determine which pieces to use for each part. Guide students to using the following rods: i. Station 1–Use the blue rod to equal one whole. ii. Station 2–Use the light green rods to model eighths. iii. Station 3–Use the dark green rod to equal one whole. 8. Monitor and assess students’ understanding as they collaborate by asking the following guiding questions: a. DOK-1 How can you partition the chocolate cake into thirds? b. DOK-1 What do you do with extra Cuisenaire Rods if you do not have one whole? c. DOK-1 Can you use a fraction in the quotient? 9. Have students rotate to the remaining stations, continue to build concrete models to solve, and record their thinking on their Student Journals.”

  • Scope 13: Area and Volume, Explore, Explore 4–Finding the Area of Composite Figures, Procedure and Facilitation Points, students show development of MP4 as they model decomposing and composing figures to find the area. “1. Read the following scenario to students: X-traordinary Landscaping Company just got some recent requests for gardens that are composite figures. This means the gardens are each in a shape that is a combination of rectangles, triangles, and/or parallelograms. They need you to use your knowledge of area formulas for each of these polygons to determine the area of the gardens shaped like composite figures. 2. Give a bag of Garden Cards to each group. 3. Have students discuss with their groups their thoughts about the definition of the term composite figure. Explain to students that a composite figure is a figure that consists of two or more geometric shapes. 4. Give a Student Journal to each student. 5. Explain to students that they will be working with their groups to determine the area of each of the eight customers’ gardens. They will decompose and rearrange the gardens into a variety of figures to help them determine the area. 6. Have students use the Garden Cards to determine the area of each customer’s garden. If the Garden cards are laminated, students can draw on the cards with dry-erase markers to show their decomposition and rearrangement of the composite figure. They will write how many of each 2-D figure the composite figure can be decomposed into. They will also use the area formulas to determine the area of each customer’s garden. 7. As students are working together, monitor their learning, and ask the following questions to check for understanding: a. DOK-2 How can you decompose this garden? b. DOK-2 Why do you need to divide by 2 to find the area for a triangle? For a trapezoid?”

  • Scope 14: Surface Area, Explore, Explore 1–Nets, Procedure and Facilitation Points, students show development of MP4 by modeling real-life situations with nets. “Part I: Nets 1. Read the following scenario to students: Tent-tastic is looking into making all of its tents out of new polyester fabric. Before the company can find out how much this will cost, Tent-tastic must create the patterns for each of the tents. Tent-tastic is challenging you to help match the pattern for each tent to its correct tent model. 2. Distribute Tent Model Cards, Pattern Cards, scissors, and tape to each group. 3. Have students work with their groups to cut out each Pattern Card and build their tents by folding and using tape. Then students will match each Tent Model Card to its three-dimensional model that was created from each Pattern Card. Note: Instruct each student in the group to cut and tape a different Pattern Card so all tents are created in a timely manner. 4. Discuss with students that these patterns are called nets. Explain that nets are the two-dimensional shapes used to create three-dimensional figures. 5. Give a Student Journal and a set of Student Journal Cutouts to each student. 6. Have students cut out the Student Journal Cutouts. Students should match the Student Journal Cutouts to their models of the tent and pattern (net). Once the cards are matched, have students glue the Student Journal Cutouts in the Student Journal. 7. While students are working, actively monitor their progress. Ask the following guiding questions: a. DOK-2 What are the attributes of this figure? b. DOK-1 What two-dimensional figures do you see on this Pattern Card? c. DOK-2 What is the relationship between the faces on each tent and the two-dimensional figures you see on its matching Pattern Card?”

MP5 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students use appropriate tools strategically as they work with the support of the teacher and independently throughout the Scopes. Examples include:

  • Scope 2: Compare and Order Rational Numbers, Explore, Explore 1–Compare Rational Numbers, Procedure and Facilitation Points, students show development of MP5 by determining when it is more useful to use a vertical versus a horizontal number line. “1. Read the following scenario to students: Jack loved seeing all the animals on his vacation! He decided to watch another animal show and record as much information as he could about it. Help Jack understand the information that he recorded by creating number lines and using comparison symbols and absolute value to understand the information. 2. Distribute the Animal Show Information Cards and one bag of index cards to each group. 3. Have students look at the Jumping Contest card. Discuss the following questions with the class: a. DOK-1 What comparison symbols can we use to compare the height that each animal jumped? b. DOK-1 What would you write to compare Sally’s jumping height to Sindy’s jumping height? c. Explain to the class about inequalities: Mathematicians call this an inequality. We will use inequalities and words to compare Jack’s recordings at the animal show. 4. Explain to students that we have previously found absolute value. In this Explore we will need to find the magnitude. Magnitude is found by taking the absolute value of a number. a. DOK-1 Jack has a debt of $5. What is this value as a rational number? b. DOK-1 Magnitude is found by taking the absolute value of a number. What is the magnitude of -5? 5. Give a Student Journal to each student. 6. Students will work collaboratively with their groups and their giant number lines on the floor to create number lines using the information from each Animal Show Information Card. Students will need to determine the intervals for each number line and write the rational numbers on the index cards. Some cards will need to be reused for different sets; for example, write 0 on one index card and use it for every number line created. Students will then use the giant number lines to determine the location of each point on the number lines on the Student Journal. Then students will write inequalities and answer the questions for each scenario. 7. As students are working, actively monitor each group. For students who are struggling, you can provide the Blank Number Lines to help them. Ask the following guiding questions: a. DOK-1 Where are negative numbers on a horizontal number line? On a vertical number line? b. DOK-1 Where are positive numbers on a horizontal number line? c. DOK-1 How can you determine the interval to use for each scenario? d. DOK-1 What should you do to plot both fractions and decimal numbers on the number line?”

  • Scope 4: Coordinate Plane Problem Solving, Explore, Explore 1–Distances Between Points, Procedure and Facilitation Points, students show development of MP5 as they use the Coordinate Plane to solve real-world problems. Students understand the limits of the coordinate grid as distance cannot be measured with a negative number. “Part I: Partner Competition 1. Read the following scenario to students: Pecan Park was holding its annual Spring Egg-Toss Competition. In the partner competition, teams consisted of a pair of participants who continued to move apart until they dropped their egg. The coordinates of each member of four different teams were recorded in a table. The coordinates reflected the positions of the partners during their last successful egg toss. The team with the greatest distance between partners was the winner of the competition. Use this information to plot each team on the coordinate plane provided and calculate the distance between the team members to determine the winner of the competition. 2. Give a Student Journal to each student. 3. Students will work in their groups to plot the location of each partner on the coordinate plane by using their colored pencils to connect each team’s coordinates with its corresponding team color. Then, students will calculate the distance between each set of partners on the map and record the distance in the table. 4. Monitor student collaboration, and use the following guiding questions to assess understanding: a. DOK-2 What do you notice about the coordinates of the Orange Team and the Green Team? b. DOK-1 What do these coordinates look like when graphed? c. DOK-1 Why are none of the distances negative? d. DOK-1 What is a mathematical term that represents a number’s distance from 0?”

  • Scope 16: Represent and Interpret Data, Explore, Explore 3–Box Plots, Procedure and Facilitation points, students show development of MP5 by using box plots to analyze a data set. Students explain their reasoning as to which type of data reporting works best based on the situation they encounter. “1. Read the following scenario: You are reporting on the Straw Tower Challenge for your school newspaper. One sixth-grade class that is participating in the Straw Tower Challenge has given you their data. Every pair of students in the class recorded the height of their straw tower on a class data chart. You will need to analyze the data given to you so that you can correctly report the results for the school newspaper. 2. Discuss the following concepts and questions with the class: a. DOK- 1 What are some of the types of graphs we have worked with so far? b. DOK-2 How were these graphs similar and different? c. Display the Class A Box Plot Card for the class. d. Explain to class: This is another type of graph that we can use called a box plot. This graph also has a unique way of organizing data. You will be examining how a box plot is set up and how it specializes in communicating measures of data in ways that the other two graphs do not. 3. Give the Student Journal and a Class A Box Plot Card to each student. 4. Students will glue the box plot in the top box on the Student Journal. Students will collaborate with their teams to explore how box plots are set up and what measures of data we can find in a box plot. Each group will collaborate to make predictions about the data from the box plot and record their thinking on the Student Journal. 5. As students are working, actively monitor the students. Ask guiding questions such as the following: a. DOK-1 What is the lowest data value? b. DOK-1 What is the highest highest data value? c. DOK-1 What do you predict is the middle value of this data? 6. Allow students enough time to complete the predictions about the data from the box plot. 7. Read the following scenario: Class A’s teacher found the data from the Straw Tower Challenge! Use these data points to determine the values of different measures of data for the Straw Tower Challenge for your report. 8. Give the Class A Data Card to each student. 9. Have students glue the Class A Data Card in the box on the Student Journal. 10. Instruct students to collaborate with their teams to determine the measures of data that they previously made predictions about. Have students circle each measure of data on the data card. a. DOK-1 What is the height of the shortest straw tower? b. DOK-1 What is the height of the tallest straw tower? c. DOK- 1 What is the height of the straw tower that is in the middle of the data?”

Indicator 2H
02/02

Materials attend to the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for STEMscopes Math Grade 6 meet expectations for supporting the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Students have opportunities to engage with the Math Practices across the year and are identified for teachers within the Standards of Mathematical Practice within the Explore sections of the Scopes. MP6 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students attend to precision as they work with the support of the teacher and independently throughout the Scopes. Examples include:

  • Scope 3: Compare and Order Rational Numbers, Explain, Show What You Know–Part 1: Compare Rational Numbers, students build experience with MP6 as they attend to precision when labeling rational numbers on vertical and horizontal number lines to help determine comparison statements. “The following temperatures were recorded last February in Boston, Massachusetts. Day 1: 0°0\degreeC; Day 2: 215°-2\frac{1}{5}\degreeC ; Day 3: 1.5°-1.5\degreeC; Day 4: 1310°1\frac{3}{10}\degreeC; Day 5: 2.2°2.2\degreeC. Question 1: Plot each temperature on the number line. Question 2: Write an inequality to compare the temperatures on days 3 and 4. Question 3: A temperature of 0℃ or below allows water to freeze. On which days did water reach the freezing point? Question 4: Between which two consecutive days was the temperature change the greatest? Justify your reasoning in relation to the number line.”

  • Scope 10: Percents, Evaluate, Mathematical Modeling Task–Savvy Shopper, Student Handout, students show development of MP6 as they attend to detail in solving real-life problems and use precise vocabulary to explain their thinking. “During the summer, Jessica saved $300 to buy herself a new school wardrobe. Her favorite store at the mall is having a back-to-school sale, and she has chosen to purchase the items below.” Students see an image of various clothing items each labeled with their cost and discount amount. “Part I 1. Will Jessica have enough money to purchase all of the items? Justify your answer.”

  • Scope 16: Represent and Interpret Data, Elaborate, Fluency Builder–Represent and Interpret Data, Procedure and Facilitation Points, students show development of MP6 as they use clear and precise language in discussion with others. “2. Model how to play the game with a student. a. Shuffle the cards, and place them face down in a stack between the players. b. Player 1 flips over one card. Both players analyze the problem and determine if the provided solution to the problem is correct and the student who answered it is a math expert or if the solution is incorrect and it is necessary to fix the mistake.”

Indicator 2I
02/02

Materials support the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for STEMscopes Math Grade 6 meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Students have opportunities to engage with the Math Practices across the year and are identified for teachers within the Standards of Mathematical Practice within the Explore sections of the Scopes. MP7 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students look for and make use of structure as they work with the support of the teacher and independently throughout the Scopes. Examples include:

  • Scope 6: Positive Rational Number Operations, Explore, Explore 4–Add and Subtract Multi-Digit Decimal Numbers, Procedure and Facilitation Points, students build experience with MP7 as they look for patterns or structures to model and solve problems while working with operations involving whole numbers, fractions, and decimals. “Part I: Open the Explore with the following class discussion where students will discover when adding decimal numbers, you first need to line up the place values. DOK-1 What is the sum of 2,412+1762,412+176? Accept all answers. Students should recall lining up place values before they begin adding. Allow students to revise their answers if needed. Come to a class consensus that 2,412+176=2,5882,412+176=2,588. DOK-1 What is the sum of 241.2+176241.2+176? Accept all answers. Students should recall lining up place values before they begin adding. Allow students to revise their answers if needed. Come to a class consensus that 241.2+176=417.2241.2+176=417.2. DOK-1 What is the sum of 241.2+17.6241.2+17.6? Accept all answers. Students should recall lining up place values before they begin adding. Allow students to revise their answers if needed. Come to a class consensus that 241.2+17.6=258.8241.2+17.6=258.8. DOK-1 What do you notice about the digits of the addends? …Read the following scenario to students: Sally’s homeroom is divided into four teams. Each team will provide a different item for the bake sale portion of the fundraiser. They are responsible for making one batch of their assigned item. Using a list of ingredients and their prices, determine the cost of each bake sale item.Give a Student Journal to each student. Have students collaborate with their groups to determine the amount that each team will need to spend in order to purchase items for the bake sale. Students will use the Bake Sale Card for the ingredients list and the Grocery Ad for pricing. As students are working, actively monitor students and provide support as needed. DOK- 1 What steps should we take to add decimal numbers together? We must first line up the decimal points and each place value. We may need to add placeholder zeros when adding two decimal numbers that have different place values. DOK- 1 What should we do when we line up decimal numbers with different place values? DOK- 1 What strategy could we use to check our answers? DOK- 1 How can you use graph paper to help you when adding decimal numbers?”

  • Scope 7: Equivalent Numerical Expressions, Evaluate, Skills Quiz, Question 1-5, students build experience with MP7 as they look for patterns and use structure to solve problems involving factors. “Solve each problem. Show or explain your mathematical thinking. 1. Find the prime factorization of 84. Write 84 as a product of its prime factors. 2. What are the first two common multiples of 4 and 5? 3. Find the greatest common factor of 52 and 68. 4. Name all common factors of 33 and 99. 5. Find the least common multiple of 6 and 8.”

  • Scope 10: Ratios, Rates, and Unit Rates, Explore, Explore 1–Ratios, Procedure and Facilitation Points, students build experience with MP7 as they look closely to discern a pattern or structure. “Read the following scenario: Trixie is picking fruit from her fruit farm to sell at the local farmers’ market fruit stand. Each week, she picks different fruits, depending on that week’s demand. She wants to keep a log of each week’s demand by representing the numbers of each type of fruit in the form of a ratio. Help her determine the ratio between each type of fruit that she brings to the market each week. Display the Fruit Stand Card for week 1. Discuss the following questions with the students:How many blueberries are there for week 1? There are 6 blueberries. How many strawberries are there for week 1? There are 8 strawberries.We want to show the relationship of strawberries to blueberries in week 1. (Write out, “There are ___ strawberries for every ___ blueberries.”) To model the relationship between strawberries and blueberries, what would we need to fill in the blanks with? In the first blank we would need to put 8 because there are 8 strawberries. In the second blank we will need to write 6 because there are 6 blueberries. Explain to class: Mathematicians call this relationship a ratio. Mathematicians write ratios in the order that the ratio asks. In this scenario, we want to represent strawberries to blueberries, therefore we write the number for strawberries in the first spot and the number for blueberries in the second spot. We can also write the ratio for the information shown on week 1s Fruit Stand Card in the following ways: “For every 8 strawberries, there are 6 blueberries”; “8:6”; “8 to 6”; or “There are 8 strawberries for every 6 blueberries.” How can we draw a tape diagram to represent the relationship between strawberries and blueberries? Draw one tape diagram with 8 spaces to represent the strawberries. Below draw a tape diagram that has only 6 spaces to represent the 6 blueberries. Model for students how to draw the tape diagram model for 8 strawberries to 6 blueberries. As you work through each week’s scenario, we will learn other ways to represent ratio relationships as well. Give one Student Journal to each student and one set of Fruit Stand Cards to each group. Students will work collaboratively to represent the information on each Fruit Stand Card. They will record the number of each type of fruit, draw a tape diagram to show the number of each type of fruit, and then write the ratio describing their models in two different ways. Provide linking cubes to students who are struggling. Have students model the ratio with linking cubes by linking the correct amount together for each fruit in the scenario. Then students can draw a model of their linking cubes as a tape diagram on the Student Journal. As students are working together, monitor their learning, and ask the following questions to check for understanding: DOK-1 What does each number in your ratio represent? DOK-1 How would the ratio of fruit for week 3 change if I added one more strawberry to the picture? DOK-1 Does the larger number always have to go second in a ratio? DOK-1 How do you know which number to put first in the ___:___ ratio? DOK-2 Is your ratio comparing part to part or part to whole? Explain how you know. DOK-2 How would this ratio change if you were comparing part to whole instead of part to part?”

MP8 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students look for and express regularity in repeated reasoning as they work with the support of the teacher and independently throughout the Scopes. Examples include:

  • Scope 12: Measurement Conversions, Evaluate, Skills Quiz, Question 2, 4, and 5, students build experience with MP8 as they use repeated reasoning when converting units of measurement. “Directions: Solve each problem. Show or explain your mathematical thinking. 2. Francisco drove 537.6 kilometers on his road trip across Texas. One mile is approximately 1.6 kilometers. Approximately how many miles did Francisco drive? 4. Convert 200 gallons to liters. (1 gallon is approximately 3.8 liters.) 5. If 1 inch is approximately 2.5 centimeters, approximately how many inches is 80 centimeters?”

  • Scope 16: Understand Variability, Explore, Explore 1–Variability in Data, Procedure and Facilitation Points, students build experience with MP8 as they use repeated reasoning to determine if a question is statistical or non-statistical. “Part II: Understanding Statistical Questions, 1. Read the following scenario to the class: The company called Survey Tiger also has a business that contacts small and big businesses to ask them questions and track the feedback they receive to these questions. Some of these questions are statistical questions, and their data and responses can vary. Other questions are non-statistical questions, and their data and responses do not vary. Survey Tiger needs your help in determining which questions they asked are statistical and non-statistical questions. 2. Quickly review the definition of a statistical question by asking the following questions: a. DOK-1 What is a statistical question? b. DOK-1 What is a survey question? c. DOK-1 Describe how data can vary. 3. Explain to the class that a statistical question can be answered with numerical data or categorical data, meaning the data can vary with numbers or different categories as a response to the question. a. DOK-2 What are some examples of data that can have various categories? b. DOK-2 What are some examples of data that can have various numbers as a response? 4. Assign each group to a station card around the room. Instruct the students to read each scenario and the questions that belong with that scenario. 5. Encourage each group to collaborate together in deciding how to sort the questions and whether the question is a statistical question and has a response with various data, or a non-statistical question and has a response of only one answer. 6. Monitor and check each group for understanding by asking the following questions: a. DOK-2 Does this question require a response with one answer or various answers? b. DOK-1 What do we call a question that requires a response with various data? c. DOK-1 What do we call a question that requires a response with only one piece of data? d. DOK-2 Can a statistical question only be answered with various numbers? Explain. e. DOK-1 What does it mean to find the average of something?”

  • Scope 18: Summarize Numerical Data, Explore, Explore 1–Mean and Median, Procedure and Facilitation Points, students build experience with MP8 as they make connections between measures of center and spread and recognize trends when interpreting graphical data representations. “Part I: Mean as Balance PointRead the following scenario to the class: José is tracking his total number of home runs and total number of hits for several series of baseball games he has played in. José wants to determine how many home runs and how many total hits he would have to have in each series to have balanced out his hits and home runs evenly between each series. Help José find the mean as a balance point to determine the number of home runs and the number of total hits he would have to have in each series to balance the home runs and total hits. Give a Student Journal to each student. Give a set of José’s Baseball Scenario Cards and linking cubes to each group.Have students discuss what the term balance point means. Explain to students that the balance point is the mean of a data set.Have students use José’s Home Runs scenario card to record the number of home runs hit in each series on the table in the Student Journal. Students will also create a dot plot to represent the number of home runs hit in each series. They will use the linking cubes to represent the data points for José’s home runs. NoteOne linking cube represents one data point (table). For example, in series 1 José has 3 home runs = 3 linking cubes. Have students stack the linking cubes to represent each series. NoteSeries 1 should have 3 cubes, series 2 should have 1 cube, series 3 should have 5 cubes, series 4 should have 5 cubes, and series 5 should have 1 cube. Once the correct number of linking cubes is stacked for each series, students should figure out how many cubes each series should have to have an equal number of home runs hit by redistributing the stacks so that each stack has an equal amount of cubes. Students will only use cubes for José’s Home Runs scenario card. Actively monitor students as they are working with their groups using the cubes to understand mean as the balance point. Ask questions such as the following: DOK-1 How can you use the linking cubes to determine the balance point? DOK-2 How do you think the balance point would be affected if we added more data points above the balance point? DOK-2 How can you interpret the mean as the balance point using a dot plot?”

Overview of Gateway 3

Usability

The materials reviewed for STEMscopes Math Grade 6 meet expectations for Usability. The materials meet expectations for Criterion 1, Teacher Supports; Criterion 2, Assessment; Criterion 3, Student Supports.

Criterion 3.1: Teacher Supports

09/09

The program includes opportunities for teachers to effectively plan and utilize materials with integrity and to further develop their own understanding of the content.

The materials reviewed for STEMscopes Math Grade 6 meet expectations for Teacher Supports. The materials: provide teacher guidance with useful annotations and suggestions for enacting the student and ancillary materials; contain adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current grade so that teachers can improve their own knowledge of the subject; include standards correlation information that explains the role of the standards in the context of the overall series; provide explanations of the instructional approaches of the program and identification of the research-based strategies; and provide a comprehensive list of supplies needed to support instructional activities. 

Indicator 3A
02/02

Materials provide teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

The materials reviewed for STEMScopes Math Grade 6 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

Materials provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials. Within each Scope, there is a Home dropdown menu, where the teacher will find several sections for guidance about the Scope. Under this menu, the Scope Overview has the teacher guide which leads the teacher through the Scope’s fundamental activities while providing facilitation tips, guidance, reminders, and a place to record notes on the various elements within the Scope. Content Support includes Background Knowledge; Misconceptions and Obstacles, which identifies potential student misunderstandings; Current Scope, listing the main points of the lesson, as well as the terms to know. There is also a section that gives examples of the problems that the students will see in this Scope, and the last section is the Coming Attractions which will describe what the students will be doing in the next grade level. Content Unwrapped provides teacher guidance for developing the lesson, dissecting the standards, including verbs that the students should be doing and nouns that the students should know, as well as information on vertical alignment. Also with each Explore, there is a Preparation list for the teacher with instructions for preparing the lesson and Procedure and Facilitation Points which lists step-by-step guidance for the lesson. Examples include:

  • Scope 10: Percents, Engage, Accessing Prior Knowledge–Four Corners, Identifying Misconceptions, provides guidance on how to identify student misconceptions. “Slide 1: Students who choose slide 1 think that a product is always greater than the multiplicands. They don’t understand that multiplying a whole number with a fraction less than 1 will result in a product less than the whole number. Slide 2: This is the correct slide. Slide 3: The students who choose this slide don’t understand that is actually equal to 1, and the product of a whole number and 1 is the same whole number. Slide 4: The students who choose this slide are multiplying the whole number with both the numerator and the denominator, which is an incorrect way of multiplying whole numbers and fractions.”

  • Scope 12: Dependent and Independent Variables, Engage, Accessing Prior Knowledge–Fact or Fiction, Description provides an instructional strategy and the purpose of the strategy. “Students will listen to prompts about the prior standard and communicate whether they feel the prompts are fact or fiction by walking to the designated sides of the classroom. This element is designed to uncover student misconceptions; it should not be taken for a grade.”

  • Scope 15: Understand Variability, Explore, Explore 1–Variability in Data, Procedure and Facilitation Points provides the teacher with guiding questions to ask students as students work. “6. Monitor and assess each group’s understanding of the task by asking the following guiding questions: a. DOK-1 What survey question will you be asking your classmates? Answers will vary. b. DOK-2 What does it mean when it says your question will be answered with data? Answers may vary. Data is information collected from individuals. c. Explain to the class: The information collected can be numerical or categorical. Numerical data is responses that are numbers. Categorical data includes responses such as favorite pizza toppings. d. DOK-3 How can you organize the data collected on the table provided on the survey document? Answers may vary depending on the survey question. I can list the classmate responses on the left side of the table and mark a tally for each classmate who responds with that response on the right side of the table. e. DOK-3 How can you use the data collected to create a dot plot? Answers may vary. I can split the dot plot into equal parts for each response and label each line with the student response. Then, for each tally represented in the table, we can place a dot above that response on the dot plot. If there are a lot of responses, we can create a key that shows that each dot on the dot plot equals 2, 3, 4, 5, etc. responses. f. DOK-1 Using the data provided by your classmates, what is the answer to your survey question? Answers will vary based on data.”

Indicator 3B
02/02

Materials contain adult-level explanations and examples of the more complex grade-level/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.

The materials reviewed for STEMScopes Math Grade 6 meet expectations for containing adult-level explanations and examples of the more complex grade/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.

Each Scope has a Content Overview with a Teacher Guide. Within the Teacher Guide, information is given about the current Scope and its skills and concepts. Additionally, each Scope has a Content Support which includes sections entitled: Misconceptions and Obstacles, Current Scope, and Coming Attractions. These resources provide explanations and guidance for teachers. Examples include:

  • Scope 2: Integers, Home, Content Support, Current Scope. It states, “Students will extend their knowledge of the number line to represent positive and negative numbers. Students reason about the relationship between a number and its opposite as points that are equidistant from zero. Both horizontal and vertical numbers will be used, as experience with both types facilitate students’ movement from number lines to coordinate grids. Students use integers to represent real-world contexts and to understand the meaning of zero in each situation. Students learn the absolute value symbol and that absolute value measures the distance from an integer to zero, and can be used to determine the distance between two numbers. Contextual problem solving, such as temperature, elevation, and banking help students relate their understanding of positive and negative values, opposites, and absolute value.”

  • Scope 6: Positive Rational Number Operations, Home, Content Overview, Teacher Guide, Vertical Alignment, Future Expectations. It states,  “Effective strategies for computation with positive rational numbers relate to a series of other sixth grade Scopes. Sixth graders will apply computation strategies when exploring measurement conversions, equations and inequalities, area, surface area, volume, and ratios. In Grade 7, students will extend operations to include negative numbers. Proficiency of number operations will effectively allow seventh-grade students to study repeating decimals, proportional relationships and scale drawings, equations and inequalities, circle measurement, and probability and sampling.”

  • Scope 12: Measurement Conversions, Home, Content Overview, Teacher Guide, Scope Summary. It states, “Within this Scope, students will grow their knowledge about measurement through using their understanding of ratio concepts and ratio reasoning to solve real-world and mathematical problems. As students progress through this Scope, they will also learn how to use ratio reasoning to convert measurement units through the manipulation and transformation of units when it is appropriate for multiplying and dividing quantities.”

  • Scope 18: Summarize Numerical Data, Home, Content Support, Coming Attractions. It states, “Students in seventh grade use random sampling to draw inferences about populations, and they investigate chance processes. They develop, use, and evaluate probability models. In eighth grade, students investigate patterns of association in bivariate data. This work extends into high school, where students continue to interpret categorical and quantitative data, and then explore conditional probability and the rules of probability.”

Indicator 3C
02/02

Materials include standards correlation information that explains the role of the standards in the context of the overall series.

The materials reviewed for STEMScopes Math Grade 6 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.

Correlation information is present for the mathematics standards addressed throughout the grade level and can be found in several places including a drop-down Standards link on the main home page, within teacher resources, and within each Scope. Explanations of the role and progressions of the grade-level mathematics are present. Examples include:

  • In each Scope, the Scope Overview, Scope Content, and Content Unwrapped provides opportunities for teachers to view content correlation in regards to the standards for the grade level as well as the math practices practiced within the Scope. The Scope Overview has a section entitled Student Expectations listing the standards covered in the Scope. It also provides a Scope Summary. In the Scope Content, the standards are listed at the beginning. This section also identifies math practices covered within the Scope. Misconceptions and Obstacles, Current Scope, and Background Knowledge make connections between the work done by students within the Scope as well as strategies and concepts covered within the Scope. Content Unwrapped again identifies the standards covered in the Scope as well as a section entitled, Dissecting the Standard. This section provides ideas of what the students are doing in the Scope as well as the important words they need to know to be successful.

  • Teacher Toolbox, Essentials, Vertical Alignment Charts, Vertical Alignment Chart Grade 5-8, provides the following information:  “How are the Standards organized? Standards that are vertically aligned show what students learn one grade level to prepare them for the next level. The standards in grades K-5 are organized around six domains. A domain is a larger group of related standards spanning multiple grade levels shown in the colored strip below: Counting and Cardinality, Operations and Algebraic Thinking,  Number and Operations in Base Ten, Number and Operations–Fractions, Measurement and Data, Geometry.” Tables are provided showing the vertical alignment of standards across grade levels.

  • Scope 8: Algebraic Expressions, Home, Scope Overview, Teacher Guide, Scope Summary, states, “As students participate in this Scope, they will extend their previous knowledge and understanding of arithmetic to algebraic expressions. By participating in the explorations within the Scope, students will learn how to read and identify parts of expressions using mathematical terms; write expressions that contain letters; and evaluate and perform expressions and arithmetic operations at specific values for their variables. Students will also learn how to apply properties of operations to create equivalent expressions and identify if two expressions are equivalent or not.”

  • Scope 15: Surface Area, Home, Content Unwrapped, Implications for Instruction, states “In this grade level, students extend their reasoning about area to include figures composed of both rectangles and triangles. Students explore properties of nets that form three-dimensional figures. They determine the surface area of a three-dimensional figure by finding the area of each face in reference to its corresponding net.”

Indicator 3D
Read

Materials provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.

The materials reviewed for STEMScopes Math Grade 6 provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement. 

The program provides an initial letter, found in the Teacher Toolbox, that can be used in conjunction with Google Documents to personalize an overview of the program. Teacher Toolbox, Parent Letter: Secondary, states, “STEMScopes is built on an instructional philosophy that centers on children acquiring a conceptual understanding of mathematics through hands-on exploration, inquiry, discovery, and analysis. Each lesson includes a series of investigations and activities to bring mathematics to life for our students so they can learn by doing and fully engage in the process. Intentional cultivation of concepts and skills solidifies our students’ ability to make relevant connections and applications in the context of the real world. Lessons are built by using the research-based 5E+IA model, which stands for Engage, Explore, Explain, Elaborate, Evaluate, Intervention, and Acceleration. Each one of these components of the lesson cycle features specific resources to support not only our students’ understanding of mathematical concepts, but also that of our teachers. STEMScopes Math features many resources for our educators, including Math Stories, Math Today, Writing in Math, Interactives, Online Manipulatives, and much more!”

Each Scope has a corresponding parent letter, in English and Spanish, that provides a variety of supports for families. Home, Parent Letter, states, ”The parent is provided a breakdown of the concepts being learned in class, along with key vocabulary terms and Math Outside the Classroom! conversation starters.” A video is provided in How To Use STEMScopes Math that provides guidance on how to use the Scope parent letter. Examples include:

  • Scope 6: Positive Rational Number Operations, Home, Parent Letter, gives a brief overview of the concepts covered in this Scope. “In math class, your student is about to explore operations with positive rational numbers. To master this skill, students will build on their knowledge of whole number, decimal, and fraction operations from fifth grade. As your student extends their knowledge of this concept throughout sixth grade, they will learn the following concepts: Fluently add, subtract, multiply, and divide multi-digit numbers using the standard algorithm. Example: Jake had 5 kilograms of sand for a science experiment. He had to measure out exactly 1.85 kilograms for a sample. How many kilograms of sand will be left after he measures out the sample? a. 6.85, b. 4.85, c. 31.5, d. 3.15, Answer choice d is correct.”

  • Scope 11: Percents, Home, Parent Letter, provides key vocabulary words that can be reviewed. ”While working with your student at home, you may find the following vocabulary terms helpful in your communication about percents. These are terms your student will be encouraged to use throughout our explorations and during our math chats, which are short, whole-group discussions at the conclusion of each activity, Terms to Know, benchmark fractions: a familiar fraction used as a reference point in order to measure, compare, and assess the reasonableness of a fractional value, double number line diagram: a pair of parallel number lines used to represent equivalent ratios, equivalent ratios: two or more ratios that are equal, multiplicative comparison: a situation in which one quantity is a certain number of times as large as another quantity; a specified number is multiplied by another number to result in a greater or lesser quantity, number line diagram: a line on which numbers are marked at intervals, percentage: a special ratio that compares a number to 100 using the percent symbol, %; a rate per 100, rate: a type of ratio where the quantities have two different units, ratio: a comparison of two quantities that shows their sizes in relation to one another, ratio language: language used to mathematically describe the relationship between any two units that are being compared in a ratio using the phrase for every… there are… or the word to, ratio relationship: equivalent ratios form a ratio relationship between the two quantities being compared, ratio table: a list of pairs of equivalent ratios used to determine the relationship between the ratios, unit rate: a rate with a denominator of 1 that shows how many units of the first type corresponds to one unit of the second type, tape diagram: a rectangular visual model that represents equal parts, used to model word problems involving part-part-whole relationships”

  • Scope 18: Summarize Numerical Data, Home, Parent Letter, provides activities that could be completed with families at home. “Math outside the Classroom! Summarizing numerical data is used all around our everyday lives. Chat about where you may summarize numerical data in your everyday life. Below are a few examples: Our brain collects data all the time. We may compare how far we walk or run each day over the course of a month. We may also compare the price of an item we want to buy between different stores or over time to determine when and where to buy the item. Talk with your student about situations in which you can collect data. Begin with a situation that applies to their life. For example, as you drive around your community, look at the price of gas at various places. Have your student write down the prices and create a dot plot with the values. Find the mean, median, and range of the data.”

Indicator 3E
02/02

Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.

The materials reviewed for STEMscopes Math Grade 6 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies. 

The Teacher Toolbox contains a Secondary STEMscopes Math Philosophy document that provides relevant research as it relates to components for the program. Examples include:

  • Teacher Toolbox, Essentials, STEMscopes Math Philosophy, Elementary, Learning within Real-World, Relevant Context, Research Summaries and Excerpts, states, “One of the major issues within mathematics classrooms is the disconnect between performing procedural skills and knowing when to use them in everyday situations. Students should develop a deeper understanding of the mathematics in order to reason through a situation, collect the necessary information, and use the mechanics of math to develop a reasonable answer. Providing multiple experiences within real-world contexts can help students see when certain skills are useful. “If the problem context makes sense to students and they know what they might do to start on a solution, they will be able to engage in problem solving.” (Carpenter, Fennema, Loef Franke, Levi, and Empson, 2015).

  • Teacher Toolbox, Essentials, STEMscopes Math Philosophy, Elementary, CRA Approach, Research Summaries and Excerpts, states “CRA stands for Concrete–Representational –Abstract. When first learning a new skill, students should use carefully selected concrete materials to develop their understanding of the new concept or skill. As students gain understanding with the physical models, they start to draw a variety of pictorial representations that mirror their work with the concrete objects. Students are then taught to translate these models into abstract representations using symbols and algorithms. “The overarching purpose of the CRA instructional approach is to ensure students develop a tangible understanding of the math concepts/skills they learn.” (Special Connections, 2005) “Using their concrete level of understanding of mathematics concepts and skills, students are able to later use this foundation and add/link their conceptual understanding to abstract problems and learning. Having students go through these three steps provides students with a deeper understanding of mathematical concepts and ideas and provides an excellent foundational strategy for problem solving in other areas in the future.” (Special Connections, 2005).” STEMscopes Math Elements states, “As students progress through the Explore activities, they will transition from hands-on experiences with concrete objects to representational, pictorial models, and ultimately arrive at symbolic representations, using only numbers, notations, and mathematical symbols. If students begin to struggle after transitioning to pictorial or abstract, more hands-on experience with concrete objects is included in the Small Group Intervention activities.”

  • Teacher Toolbox, Essentials, STEMscopes Math Philosophy, Elementary, Collaborative Exploration, Research Summaries and Excerpts, states, “Our curriculum allows students to work together and learn from each other, with the teacher as the facilitator of their learning. As students work together, they begin to reason mathematically as they discuss their ideas and debate about what will or will not work to solve a problem. Listening to the thinking and reasoning of others allows students to see multiple ways a problem can be solved. In order for students to communicate their own ideas, they must be able to reflect on their knowledge and learn how to communicate this knowledge. Working collaboratively is more reflective of the real-world situations that students will experience outside of school. Incorporate communication into mathematics instruction to help students organize and consolidate their thinking, communicate coherently and clearly, analyze and evaluate the thinking and strategies of others, and use the language of mathematics.” (NCTM, 2000)

  • Teacher Toolbox, Essentials, STEMscopes Math Philosophy, Elementary, Promoting Equity, Research Summaries and Excerpts, states, “Teachers are encouraged throughout our curriculum to allow students to work together as they make sense of mathematics concepts. Allowing groups of students to work together to solve real-world tasks creates a sense of community and sets a common goal for learning for all students. Curriculum tasks are accessible to students of all ability levels, while giving all students opportunities to explore more complex mathematics. They remove the polar separation of being a math person or not, and give opportunities for all students to engage in math and make sense of it. “Teachers can build equity within the classroom community by employing complex instruction, which uses the following practices (Boaler and Staples, 2008): Modifying expectations of success/failure through the use of tasks requiring different abilities, Assigning group roles so students are responsible for each other and contribute equally to tasks, Using group assessments to encourage students' responsibility for each other's learning and appreciation of diversity” “A clear way of improving achievement and promoting equity is to broaden the number of students who are given high-level opportunities.” (Boaler, 2016) “All students should have the opportunity to receive high-quality mathematics instruction, learn challenging grade-level content, and receive the support necessary to be successful. Much of what has been typically referred to as the "achievement gap" in mathematics is a function of differential instructional opportunities.” (NCTM, 2012).” STEMscopes Math Elements states, “Implementing STEMscopes Math in the classroom provides access to high quality, challenging learning opportunities for every student. The activities within the program are scaffolded and differentiated so that all students find the content accessible and challenging. The emphasis on collaborative learning within the STEMscopes program promotes a sense of community in the classroom where students can learn from each other.”

Indicator 3F
01/01

Materials provide a comprehensive list of supplies needed to support instructional activities.

The materials reviewed for STEMScopes Math Grade 6 meet expectations for providing a comprehensive list of supplies needed to support instructional activities. 

The Teacher Toolbox provides a Secondary Materials List that has a spreadsheet with tabs for each grade level, 6-8. Each tab lists the materials needed for each activity within each Scope for the grade level. Within each Scope, the Home Tab also provides a material list for all activities. It allows the teacher to input the number of students, groups, and stations, and then calculates how many of each item is needed.  Finally, each activity within a Scope has a list of any materials that are needed for that activity. Examples include:

  • Scope 2: Integers, Elaborate, Fluency Builder–Integers, Materials, “Printed, 1 Go Fish! Instruction Sheet (per pair), 1 Set of Go Fish! Cards (per pair), Reusable, 1 Envelope or bag (per pair)”

  • Scope 6: Positive Rational Number Operations, Explore, Explore 3–Division of Fractions, Materials, “Printed, 1 Student Journal (per student), 1 Set of Tablecloth Fabric Cards (per group), 1 Exit Ticket (per student), Reusable, 1 Resealable bag (per group), 1 Set of colored pencils (per student, optional)”

  • Scope 11: Percents, Explore, Explore 3–Finding the Price and Discount, Materials, “Printed, 1 Student Journal (per student), 1 Percent Model Work Mat (per station), 1 Set of Sale Cards (per class), 1 Exit Ticket (per student), Reusable, 1 Dry-erase marker (per station), 1 Clear sheet protector (per station)”

Indicator 3G
Read

This is not an assessed indicator in Mathematics.

Indicator 3H
Read

This is not an assessed indicator in Mathematics.

Criterion 3.2: Assessment

09/10

The program includes a system of assessments identifying how materials provide tools, guidance, and support for teachers to collect, interpret, and act on data about student progress towards the standards.

The materials reviewed for STEMscopes Math Grade 6 meet expectations for Assessment. The materials identify the content standards but do not identify the mathematical practices assessed in assessments. The materials provide multiple opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance, and suggestions for following-up with students. The materials include opportunities for students to demonstrate the full intent of grade-level standards and mathematical practices across the series. 

Indicator 3I
01/02

Assessment information is included in the materials to indicate which standards are assessed.

The materials reviewed for STEMscopes Math Grade 6 partially meet expectations for having assessment information included in the materials to indicate which standards are assessed.

The materials identify grade-level content standards within the Assessment Alignment document for the Skills Quiz Alignment and Standards-Based Assessment Alignment. The Benchmark Blueprint document provides grade-level content standards alignment for the Pre-Assessment, Mid- Assessment, and Post-Assessment. While the mathematical practices are identified in each Scope within the Explores, they are not aligned to assessments or assessment items. Examples include:

  • STEMscopes Math: Common Core Sixth Grade Teacher Resources, Assessment Alignment, Assessment Alignment, Skills Quiz Alignment, identifies Scope 3: Coordinate Planes, Question 2 as addressing 6.G.3. Scope 3: Coordinate Planes, Evaluate, Skills Quiz, Question 2, “Describe the relationship between the following points: A=(112,4)A=(-1\frac{1}{2},4) and B=(112,4)B=(1\frac{1}{2},4). ___.”

  • STEMscopes Math: Common Core Sixth Grade Teacher Resources, Assessment Alignment, Assessment Alignment, Standards-Based Assessment Alignment, identifies Scope 6: Equivalent Numerical Expressions, Question 1 as addressing 6.EE.1. Scope 6: Equivalent Numerical Expressions, Evaluate, Standards-Based Assessment, Question 1, “China and India each have more than 10910^9 people. What is the value of 10910^9? Enter your answer below. ____”

  • STEMscopes Math: Common Core Sixth Grade Teacher Resources, Assessment Alignment, Benchmark Blueprint, Grade 6 Mid-Assessment, identifies Question 2 as addressing 6.NS.6.A. STEMscopes Math: Common Core Sixth Grade Teacher Resources, Resources, Benchmark Assessments, STEMscopes Math Grade 6 Mid-Assessment, Question 2, “Which is the opposite of the opposite of –10? 10-10, 00, 110\frac{1}{10}, 1010.”

Indicator 3J
04/04

Assessment system provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The materials reviewed for STEMScopes Math Grade 6 meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. 

In Grade 6, each Scope has an activity called Decide and Defend, an assessment that requires students to show their mathematical reasoning and provide evidence to support their claim. A rubric is provided to score Understanding, Computation, and Reasoning. Answer keys are provided for all assessments including Skills Quizzes and Technology-Enhanced Questions. Standards-Based Assessment answer keys provide answers, potential student responses to short answer questions, and identifies the Depth Of Knowledge (DOK) for each question. 

After students complete assessments, the teacher can utilize the Intervention Tab to review concepts presented within the Scopes’ Explore lessons. There are Small-Group Intervention activities that the teacher can use with small groups or all students. Within the Intervention, the lesson is broken into parts that coincide with the number of Explores within the Scope. The teacher can provide targeted instruction in areas where students, or the class, need additional practice. The program also provides a document in the Teacher Guide for each Scope to help group students based on their understanding of the concepts covered in the Scope. The teacher can use this visual aide to make sure to meet the needs of each student. Examples include:

  • Scope 7: Equivalent Numerical Expressions, Evaluate, Standards-Based Assessment, Answer Key, Question 6, provides a possible way a student might complete the problem. “There are 90 apples and 75 bananas available to make fruit baskets. Each basket has the same number of pieces of fruit. What is the greatest amount of fruit baskets that can be made with no fruit left over? How many pieces of fruit are in each basket? Write an expression using the distributive property. Explain your reasoning. Enter your answer in the box. (DOK-3) 15 baskets with 6 apples and 5 bananas. The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90. The factors of 75 are 1, 3, 5, 15, 25, and 75. The greatest common factor for 90 and 75 is 15, so the greatest number of baskets that can be made is 15. 15(6+5)15(6+5), so there will be 15 baskets and each basket will have 6 apples and 5 bananas.”(6.NS.4)

  • Scope 13: Dependent and Independent Variables, Evaluate, Standards-Based Assessment, Answer Key, Question 4, Part C, provides a possible solution a student might provide. “Which variable, t or d, is the independent variable, and which variable is the dependent variable? Is there more than one answer? Explain your reasoning. Enter your answer in the box. (DOK-3) The independent variable is t. Time, t, is the independent variable, and distance, d, is the dependent variable because the distance depends on the number of hours traveled” (6.EE.9)

  • Scope 16: Understand Variability, Intervention, Skill Review and Practice, Review, “Try It, Prices for candy bars at a local store are as follows: $1.00, $0.75, $1.75, $1.50, $1.50, $2.00, $1.00, $0.50, $1.50, $1.25, $1.50. Make a frequency table by listing the responses in order and make tally marks for each time the price occurs. Make a dot plot below to represent the data in the table.”

Indicator 3K
04/04

Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.

The materials reviewed for STEMscopes Math Grade 6 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series. 

Assessment opportunities are included in the Exit Tickets, Show What You Know, Skills Quiz, Technology-Enhanced Questions, Standards-Based Assessment, and Decide and Defend situations. Assessments regularly demonstrate the full intent of grade-level content and practice standards through a variety of item types, including multiple choice, multiple response, and short answer. While the MPs are not identified within the assessments, MPs are described within the Explore sections in relation to the Scope. Examples include:

  • Scope 3: Compare and Order Rational Numbers, Evaluate, provides opportunities for students to demonstrate the full intent of 6.NS.7b, “Write, interpret, and explain statements of order for rational numbers in real-world contexts.” Question 1, “A proton has a charge of +1+1, and an electron has a charge of 1-1. Which statement is true about the values of the charges? 1>+1−1>+1 because 1-1 is to the right of +1+1.; 1<+1-1<+1 because 1-1 is to the right of +1+1.; 1>+1-1>+1 because 1-1 is to the left of +1+1.; 1<+1-1<+1 because 1-1 is to the left of +1+1.” Question 2, “The temperature on the weekend was 2°-2\degreeC on Friday, 8°-8\degreeC on Saturday, and 4°-4\degreeC on Sunday. Which statements are true? Select all that apply. Saturday was the warmest day.; Sunday was colder than Friday.; Friday was warmer than Saturday.; Friday was the coldest day.” Question 3, “A diver starts at sea level. He dives down to 65 feet below sea level and then swims up to 25 feet below sea level. After a few minutes, he dives back down to a depth of 55 feet below sea level. What is the greatest depth of the diver? Enter your answer below. ____”

  • Scope 8: Algebraic Expressions, Evaluate, Standards-Based Assessment, provides opportunities for students to demonstrate the full intent of 6.EE.2, “Write, read, and evaluate expressions in which letters stand for numbers.” Question 1, “A company rents bicycles for $25 per hour. There is also a $40 fee for required insurance. Which expression represents the total cost of renting a bicycle for h hours? 25h+4025h+40; h÷25+40h\div25+4040h+2540h+25; h÷40+25h\div40+25” Question 7, “Five days a week, Mack runs m minutes on a treadmill and lifts weights for 20 minutes. The expression 5(m+20)5(m+20) represents the weekly length of Mack’s workout. Write an equivalent expression for this time. Enter your answer below. ____” Mathematical Modeling Task - Who Is Correct?, Question 1, “The first expression they have is 6g+12m2g+8t+2t6g+12m-2g+8t+2t. Juan says this expression simplified is 16g+10t16g+10t. Carlos says the equivalent expression is 4g+12m+10t4g+12m+10t. Explain who is correct. ____”

  • Scope 18: Summarize Numerical Date, Evaluate, Skills Quiz, Question 1, provides students with an opportunity to demonstrate MP5, “Use appropriate tools strategically, as they decide and explain which model they would use to display data collected.” “1. Jillian collected data to find out the leg span of each student in her class. She wants to display the data so that each student can see how their individual measurement compared with the others in the class. Should she choose to represent the data using a dot plot, box plot, or histogram? Explain your reasoning.”

Indicator 3L
Read

Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

The materials reviewed for STEMScopes Math Grade 6 provide assessments which offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment. 

STEMScopes Math provides assessment guidance in the Teacher Guide within the Scope Overview. “STEMScopes Tip, the Evaluate section, found along the Scope menu, contains assessment tools designed to help teachers gather the data they need to determine whether intervention or acceleration is warranted. From standards-based assessments to an open-ended reasoning prompt, there is an evaluation for every student’s learning style.” Examples include:

  • Students completing any assessment digitally have several options available to assist with completing the assessment. A ribbon at the top of the assessment allows the student to: change the font size, have directions and problems read which the teacher can turn on and off, highlight information, use a dictionary as allowed by the teacher, and use a calculator. If a paper copy is being used, the teacher can edit the assessment within Google Documents to change the font size and change the layout. Assessments are also available in Spanish. Teachers also can create their own assessments from a question bank allowing for a variety of assessments students can complete to show understanding. 

  • Each Scope provides an Exit Ticket to check student understanding. After reviewing answers, the teacher can use the Intervention tab online either in a small group setting or with the entire class. The Small Group Instruction activity provides more practice with the concept(s) taught within the Scope.

  • Within the Intervention tab, teachers can click on different supplemental aids that could be used to assist students completing an assessment. Examples of supplemental aids include open number lines, number charts, base tens, place value charts, etc. Teachers can decide to use these aids with students needing additional support.

Criterion 3.3: Student Supports

08/08

The program includes materials designed for each student’s regular and active participation in grade-level/grade-band/series content.

The materials reviewed for STEMscopes Math Grade 6 meet expectations for Student Supports. The materials provide: strategies and supports for students in special populations and for students who read, write, and/or speak in a language other than English to support their regular and active participation in learning grade-level mathematics; multiple extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity; and manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

Indicator 3M
02/02

Materials provide strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.

The materials reviewed for STEMscopes Grade 6 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics.

Within the Teacher Toolbox, under Interventions, materials regularly provide strategies, supports, and resources for students in special populations to help them access grade-level mathematics. Within each Explore section of the Scopes there are Instructional Supports and Language Acquisition Strategy suggestions specific to the Explore activity. Additionally, each Scope has an Intervention tab that provides support specific to the Scope. Examples include:

  • Teacher Toolbox, Interventions, Interventions–Adaptive Development, Generalizes Information between Situations, supplies teachers with teaching strategies to support students with difficulty generalizing information. “Unable to Generalize: Alike and different–Ask students to make a list of similarities and differences between two concrete objects. Move to abstract ideas once students have mastered this process. Analogies–Play analogy games related to the scope with students. This will help create relationships between words and their application. Different setting–Call attention to vocabulary or concepts that are seen in various settings. For example, highlight vocabulary used in a math problem. Ask students why that word was used in that setting. Multiple modalities–Present concepts in a variety of ways to provide more opportunities for processing. Include a visual or hands-on component with any verbal information.”

  • Scope 9: Equations and Inequalities, Explore, Explore 2–Write and Solve Equations, Instructional Supports states, “1. Struggling students may grasp the concept of the problem but have difficulty computing with decimals. Have students break down the decimals into smaller steps to solve. 2. Struggling students may have difficulty grasping why we multiply by the reciprocal when a variable is multiplied by a fraction. Use manipulatives to help them grasp the concept. For example, have students line up beans 4 by 5 making a total of 20 beans. Ask students to then isolate one-fourth of the beans (5 beans). Help students see that to get back to 20 beans they have to multiply the 5 beans 4 times (the reciprocal) making 4 sets of 5 beans, which is 20 beans.”

  • Scope 14: Area and Volume, Explore, Explore 2–Finding the Area of Quadrilaterals, Instructional Supports states,  “1. To ensure understanding of the concept of area over the mechanical application of the formula, point out that the unit squares can be used to determine area as well since area is the space covered by a closed flat shape and it takes x unit squares to cover the space. 2. Struggling students may have difficulty conceptualizing the height of the parallelogram and the triangle. As a rule of thumb, tell them that the base and height are always perpendicular to one another, and allow them to identify and mark with a highlighter the base and height of the figure to ensure that they are perpendicular to one another.”

Indicator 3N
02/02

Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.

The materials reviewed for STEMscopes Math Grade 6 meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.

Within each Scope, Scope Overview, Teacher Guide, a STEMscopes Tip is provided. It states,  “The acceleration section of each Scope, located along the Scope menu, provides resources for students who have mastered the concepts from the Scope to extend their mathematical knowledge. The Acceleration section offers real-world activities to help students further explore concepts, reinforce their learning, and demonstrate math concepts creatively.” Examples include:

  • Scope 6: Positive Rational Number Operations, Acceleration, Would You Rather–Forest Scout Fundraiser states, “Use mathematical reasoning and creativity to justify your answer to the Would You Rather question. Thomas and Ayaan are Forest Scouts and are raising money for the Scouts’ annual camping trip. They are working in teams selling chocolate bars. You have the option to join Team Oak or Team Spruce to sell Chocolate bars. Would you rather join Team Oak or Team Spruce? Justify your reasoning with mathematics. Team Oak Sold 45\frac{4}{5} of 18 boxes of milk chocolate bars Cost: $2.00 per box  Team Spruce Sold 13\frac{1}{3} of 12 boxes of milk chocolate bars with almonds Cost: $3.00 per box”

  • Scope 9: Equations and Inequalities, Acceleration, Would You Rather–Magazine Subscriptions states,  “Use mathematical reasoning and creativity to justify your answer to the Would You Rather question. Crazy Sports Car Magazine is offering different subscription plans to potential customers. They are offering potential customers the opportunity to pay $99.00 for a yearly subscription that comes with one magazine per month.  Their other plan allows potential customers to pay $9.00/month to receive one magazine per month with the option to cancel anytime. Would you rather pay for a yearly subscription or pay a monthly fee for a Crazy Sports Car Magazine subscription? Justify your reasoning with mathematics.” 

  • Scope 17: Represent and Interpret Data, Acceleration, Would You Rather–Shopping for New TVs states,  “Use mathematical reasoning and creativity to justify your answer to the Would You Rather question. Amari is interested in purchasing TVs that measure at least 50 inches for his new home. He is looking at TVs at Pete’s Electronics store and the Shop Smart store and is trying to determine which store offers the best selection of TVs by size. Would you rather recommend that Amari shops at Pete’s Electronics store or the Shop Smart store? Justify your answer by describing the distribution data.”

Indicator 3O
Read

Materials provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.

The materials reviewed for STEMscopes Math Grade 6 provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.  

Each Scope Overview highlights the potential types of work students will accomplish within the lessons. The Scope Overview states, “What Are Problems? Within the context of a scope, elements that fit into the category of problems expose students to new mathematical concepts by adhering to constructivist principles. Students are expected to explore, question, and attain conceptual understanding through engaging in these elements with teacher facilitation. What Are Exercises? Elements that have been classified as exercises have been designed to provide opportunities for students to apply their understanding to attain mastery. These are carefully sequenced to build upon students’ prior knowledge to support new skills and range in purposes, from building fluency and addressing misconceptions to applying the skill to create a plan or a product in the context of real life.” Examples include:

  • Teacher Toolbox, Mathematical Practices, Rubrics for Mathematical Practices–Sixth through Eighth Grades, Sixth Grade, Rubrics for Mathematical Practices states, “MP.3 Construct viable arguments and critique the reasoning of others. Students construct arguments by using verbal or written explanations accompanied by expressions, equations, and models, including data displays such as graphs, tables, etc., that support their conclusions. They further refine their mathematical communication skills through mathematical discussions in which they critically evaluate their own thinking and the thinking of other students. Students use various strategies to solve problems, and they defend and justify their work with others. Students may ask their peers and respond to questions such as “How did you get that?” “Why is that true?” and “How did you decide to use that strategy?” Students explain and justify their thinking to others, and they respond to others’ thinking.”

  • Scope 3: Compare and Order Rational Numbers, Elaborate, Interactive Practice–Mars Rover, is an online activity with the directions: “Welcome to Mars. You are in charge of taking the rover around the surface of Mars to locate probes. At ten different locations you will need to determine the location of two probes, which might be above you in the atmosphere, or below you in the ground. Using positive and negative integers you will need to figure out which probe is higher and which is farther away from your rover.”  For example, given a picture of the rover with two dots labeled “Probe” under the ground, “Sector Charlie: For this sector, determine which probe is higher, which is lower and which is farther away from the rover. Probe Charlie 1=61=-6 meters, >, <, ?, Probe Charlie 2=42=-4 meters, ____ is farther from the rover”

  • Scope 12: Measurement Conversions, Elaborate, Fluency Builder–Convert between Measurement Systems states, “BAM! Bam! Instruction Sheet Play this game with a partner. You Will Need: 1 Set of Bam! Cards (per pair), 1 Jar or other container (per pair), How to Play: 1. Fold the cards in half, and place them in the jar. 2. Player 1 pulls out a card from the jar and hands it to player 2. 3. Player 2 will read the question aloud for player 1 to solve. 4. Player 2 can check the answer from player 1 at the bottom of the card. 5. If a player gets a problem correct, they keep the card. If they are incorrect, the other player keeps the card. 6. Note: If the card contains an image such as a graph or a number line, the player asking the question can show the image while covering up the answer with their hand. 7. If a player pulls out a Bam! picture card, all of that player’s cards go back into the jar. 8. Players take turns pulling cards from the jar and answering questions until time is up. 9. Players must try to get as many cards as they can before time is up. 10. The player with the most cards wins.” For example, “1 fl. oz. = 30 mL, 10 mL = ____ fl. oz., Answer: 0.33 fl. oz.”

Indicator 3P
Read

Materials provide opportunities for teachers to use a variety of grouping strategies.

The materials reviewed for STEMscopes Math Grade 6 provide opportunities for teachers to use a variety of grouping strategies.

Suggestions and guidance are provided for teachers to use a variety of groupings, including whole group, small group, pairs, or individual. Examples include:

  • Scope 4: Coordinate Planes, Explore, Explore 2–Reflections on a Coordinate Plane, Preparation states,“Plan to divide the class into groups of 4.”

  • Scope 8: Algebraic Expressions, Explore, Explore 2–Simplify Expressions, Preparation states, “Plan to put students into groups of 2 or 3 to complete this activity.”

  • Scope 11: Percents, Explore, Explore 2–Solving Percent Problems Using Benchmark Fractions and Percents, Preparation states, “Plan to divide the class into groups of 3 or 4 students.”

Indicator 3Q
02/02

Materials provide strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

The materials reviewed for STEMscopes Math Grade 6 meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics. 

Within the Teacher Toolbox, the program provides resources to assist MLLs when using the materials.  The materials state, “In the curriculum, we have integrated resources to support teachers and families. Below are a few features and elements that can be used to support students at their level and provide an opportunity for families and caregivers to engage in student learning.” Examples include but are not limited to:

  • “Proficiency Levels by Domain – In this section, you will find a snapshot of language application across domains at different proficiency levels. Teachers can use this tool to help identify a student’s English proficiency level by analyzing how students are able to interpret and produce language.”  

  • “Working on Words – This open-ended activity allows students to take agency and accountability for their growing vocabulary. This activity also encourages making relevant, personal connections to new terms in different ways, such as identifying cognates.” 

  • “Sentence Stems/Frames – Students are able to practice engaging in purposeful discussion. These sentence stems and sentence frames can be used for different intents, such as asking for clarification, defending their thinking, and explaining their responses.” 

  • “Integrated Accessibility Features – Across the curriculum, we have embedded tools that allow students to listen to text being read, find the definition of words in the moment, make notes, and highlight words and phrases.” 

  • “Parent Letters – Each scope includes a letter tailored to caregivers in which the content of a scope, including its vocabulary, is explained in simplified terms. Within the Parent Letters, we have included an activities section called Tic-Tac-Toe–Try This at Home that students can engage in along with their families. This letter is written in two languages.” 

  • “Tiered Supports – Within each Explore lesson, we have included tiered supports and strategies that can be applied during the lesson for students at each proficiency level. These range in focus across all domains.” 

  • “Language Connections – Every scope has three Language Connection activities, one at each proficiency level. Language Connections meets the students at their proficiency level by providing teachers with prompts to support students in demonstrating their understanding in each language domain.” 

  • “Virtual Manipulatives – Students are able to use these across the curriculum to help them justify their answers when expressive language may be limited. These can also be used as tools for creating meaningful connections to vocabulary terms and skills.” 

  • “Visual Glossary/Picture Vocabulary – Students are able to combine visual representations and mathematical terms using student-friendly language.” 

  • “Distance Learning Videos – Major skills and concepts are broken down in these student- facing videos. Students and caregivers alike can engage in the activities at home at their own pace and incorporate familiar objects. In this way, students can apply their own language to math.” 

  • “My Math Thoughts/Math Story – These literary elements give students the opportunity to practice reading and writing about math. Students can apply reading strategies to aid with comprehension and practice not just math vocabulary, but situational vocabulary as well.”

Guidance is also provided throughout the scopes to guide the teacher. Examples include:

  • Scope 2: Integers, Explore, Explore 2–Absolute Value where students will use their knowledge of number lines to recognize that the absolute value of a positive or negative integer is the distance that number is away from zero. There lies a Language Acquisition Supports segment that provides strategies for fostering students' language development. For example “Students will enhance language attainment as they acquire knowledge from a variety of multimedia instructional formats. Beginner: Before the lesson, display images of different sports, including football, and have students repeat the sports names after you. Then share that they will create a football field on paper. Intermediate: Before the lesson, show students a clip from a football game to help them visualize the context for the Explore. Pause the clip intermittently to point out important features such as the football, the football field, helmets, etc. Advanced: Before the lesson, allow students to play a virtual football game to help them understand the sport mentioned in the Explore.”

  • Scope 12: Measurement Conversions, Explore, Explore 2–Two-Step Measurement Conversions where students will solve two-step word problems using ratio reasoning to convert measurement units within the standard measurement system or within the metric measurement system. There lies a Language Acquisition Supports segment that provides strategies for fostering students' language development. For example “Students will use support from visual cues, peers, and teachers to develop vocabulary, language structure, and background knowledge needed to comprehend written text. Beginner: Prior to the lesson, use the word convert in several sentences along with diagrams or images. Then explain to students that today they will continue to convert one unit of measurement to another. Intermediate: As a pre-lesson activity, use the word convert in several sentences along with diagrams or images. Explain to students that today they will continue to convert one unit of measurement to another. Have students create a vocabulary square for the word convert. The four sections of the square should include, Definition, Sentence, Image, and Non-example. Provide the definitions for students and encourage them to rewrite the definition in their own words underneath. Advanced: As a pre-lesson activity, use the word convert in several sentences along with diagrams or images. Then explain to students that today they will continue to convert one unit of measurement to another. Have students create a vocabulary square for conversions. The four sections of the square should include, Definition, Sentence, Image, and Non-example.”

  • Scope 16: Understand Variability, Explore, Explore 1–Variability in Data where Students will determine the difference between a statistical and a non-statistical question and explain that both require data but a statistical question has data that varies. There lies a Language Acquisition Supports segment that provides strategies for fostering students' language development. For example “Students will use support from visual cues, peers, and teachers to develop vocabulary, language structure, and background knowledge needed to comprehend written text. Beginner: As a pre-lesson activity, teach students the word survey by conducting a survey as a class. The question could be: What's your favorite color? Create a dot plot on the board as students share their responses. Explain that we're going to learn more about surveys as part of today's lesson. Intermediate: As a pre-lesson activity, read a short blurb about surveys to students then ask them how many times they heard the word survey read. Create a dot plot based on the range of guesses, then reveal the actual number. Advanced: As a post-lesson activity, give students two differently colored index cards. On one color index card will be written the word statistical and on the other color index card will be written the word nonstatistical. Show students a series of questions; students will choose which card to raise for each question. If there are discrepancies in cards raised, have students defend their answers.”

Indicator 3R
Read

Materials provide a balance of images or information about people, representing various demographic and physical characteristics.

The materials reviewed for STEMscopes Math Grade 6 provide a balance of images or information about people, representing various demographic and physical characteristics. 

While there are not many pictures in the materials students use, the images provided do represent different skin tones, hairstyles, and clothing styles. Also, there are a wide variety of names used throughout the materials. Examples include:

  • Scope 6: Equivalent Numerical Expressions, Engage, Accessing Prior Knowledge–Agree or Disagree, Procedure and Facilitation Points, depicts individuals who could be different races or ethnicities. “7. Discuss the responses as a class. Allow students to explain their reasonings for each problem. a. Disagree with Arya b. Disagree with Sarah c. Agree with Zoey”

  • Scope 9: Ratios, Rates, Unit Rates, Evaluate, Standards-Based Assessments, Question 5 depicts an individual who could be of a different race or ethnicity. “Jacques mows 32 lawns each week and makes $1,280. He charges the same rate for each lawn. Part A How much money does Jacques earn for mowing 12 lawns? Explain your reasoning. Enter your answer below. ____”

  • Scope 15: Understand Variability, Elaborate, Spiraled Review–Top-Secret Tropical Paradise Punch, Student Handout, depicts an individual who could be of a different race or ethnicity. “It’s the end of the year and time to party! The end of the year is the best time to celebrate accomplishments and often goodbyes as friends move on to different schools or places. The sixth-grade student committee is planning an end-of-the-year celebration for their grade level with Mr. Ramirez. They have decided on a tropical-themed celebration. The students will be offered fresh flower crowns, they will have the opportunity to take a selfie in a beach-themed photo booth, and steel drums will play during the celebration.”

Indicator 3S
Read

Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The materials reviewed for STEMscopes Math Grade 6 provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The program provides a list of language acquisition tools and resources. All components of the program are offered in both English and Spanish, including the Introductory Parent Letter and the Parent Letters within each Scope. Examples include:

  • Scope 8: Algebraic Expressions, Parent Letter, Description states,  “The parent is provided a breakdown of the concepts being learned in class, along with key vocabulary terms and Math Outside the Classroom! conversation starters.”

  • Teacher Toolbox, Multilingual Learners, Linguistic Diversity states, “In the curriculum, we have integrated resources to support teachers and families. Below are a few features and elements that can be used to support students at their level and provide an opportunity for families and caregivers to engage in student learning.” These resources include, but are not limited to: Working on Words, Sentence Stems/Frames, Integrated Accessibility Features, and Language Connections. 

Indicator 3T
Read

Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

The materials reviewed for STEMscopes Math Grade 6 provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

The program is available in Spanish, and includes a number of cultural examples within the materials. Examples include:

  • Scope 2: Integers, Evaluate, Standards-Based Assessment, Question 3 states, “3. On the first down of a football game, a team ran the ball for 5 yards. On the second down, the team ran the ball for the opposite number of yards. Which integer represents how many yards were run on the second down? Enter your answer in the box.”

  • Scope 7: Equivalent Numerical Expressions, Elaborate, Spiraled Review–Brrr, It’s Cold in January in Toronto, Canada states, “Toronto, Canada, is known for producing some of the best athletes in ice hockey. Ice hockey is played both inside and outside. Shaina wanted to practice hockey on the frozen pond behind her house in January. She decided the best days to practice would be on the days with the least change in temperature. Starting on January 1st, Shaina kept track of the daily high and low temperatures, in degrees Celsius. She plotted temperature changes on the coordinate plane shown below. The horizontal axis represents each day during the first week of January, and the vertical axis represents the high and low temperatures. The high temperatures are plotted in red, and the low temperatures are plotted in blue. So far, Shaina has recorded high and low temperatures for the first 4 days. It sure is cold in Toronto, Canada! Take a look at the results. What observations can you make?”

  • Scope 10: Ratios, Rates, and Unit Rates, Explore, Explore 1–Ratios, Exit Ticket, Question 1 states,  “There are 5 blueberry bushes for every 3 raspberry bushes on the farm. Draw a model to show the ratio between the amount of blueberry bushes and raspberry bushes on the fruit farm. Write a ratio to describe your model.”

Indicator 3U
Read

Materials provide supports for different reading levels to ensure accessibility for students.

The materials reviewed for STEMscopes Math Grade 6 provide supports for different reading levels to ensure accessibility for students.

The Teacher Toolbox has a tab entitled, Multilingual Learners, Linguistic Diversity, that highlights some of the options to help students at different reading levels. Examples include:

  • Teacher Toolbox, Multilingual Learners, Linguistic Diversity, Language Acquisition Progression states, “Each student’s journey to acquiring a new language is unique. A common misconception is that language acquisition is linear. However, the process is continuous and open-ended and it differs across language domains (listening, speaking, reading, and writing) depending on factors such as context or situation, with whom the learner is engaging, and how familiar the student is with the topic. The Proficiency Levels by Domain provide an overview of how students are applying language across different domains, as well as methods and tools that can be applied to provide support. The skills and strategies provided are meant to build upon each other as students progress through the levels.

  • Teacher Toolbox, Multilingual Learners, Linguistic Diversity, Resources and Tools states, “In the curriculum, we have integrated resources to support teachers and families. Below are a few features and elements that can be used to support students at their level and provide an opportunity for families and caregivers to engage in student learning. Proficiency Levels by Domain – In this section, you will find a snapshot of language application across domains at different proficiency levels. Teachers can use this tool to help identify a student’s English proficiency level by analyzing how students are able to interpret and produce language. Working on Words – This open-ended activity allows students to take agency and accountability for their growing vocabulary. This activity also encourages making relevant, personal connections to new terms in different ways, such as identifying cognates. Sentence Stems/Frames – Students are able to practice engaging in purposeful discussion. These sentence stems and sentence frames can be used for different intents, such as asking for clarification, defending their thinking, and explaining their responses. Integrated Accessibility Features – Across the curriculum, we have embedded tools that allow students to listen to text being read, find the definition of words in the moment, make notes, and highlight words and phrases. Parent Letters – Each scope includes a letter tailored to caregivers in which the content of a scope, including its vocabulary, is explained in simplified terms. Within the Parent Letters, we have included an activities section called Tic-Tac-Toe –Try This at Home that students can engage in along with their families. This letter is written in two languages. Tiered Supports – Within each Explore lesson, we have included tiered supports and strategies that can be applied during the lesson for students at each proficiency level. These range in focus across all domains. Language Connections – Every scope has three Language Connection activities, one at each proficiency level. Language Connections meets the students at their proficiency level by providing teachers with prompts to support students in demonstrating their understanding in each language domain. Virtual Manipulatives – Students are able to use these across the curriculum to help them justify their answers when expressive language may be limited. These can also be used as tools for creating meaningful connections to vocabulary terms and skills. Visual Glossary/Picture Vocabulary – Students are able to combine visual representations and mathematical terms using student-friendly language. Distance Learning Videos – Major skills and concepts are broken down in these student-facing videos. Students and caregivers alike can engage in the activities at home at their own pace and incorporate familiar objects. In this way, students can apply their own language to math. Skills Quiz – This element utilizes just the numbers! This allows teachers to assess a student’s understanding without a language barrier. My Math Thoughts/Math Story – These literary elements give students the opportunity to practice reading and writing about math. Students can apply reading strategies to aid with comprehension and practice not just math vocabulary, but situational vocabulary as well. Daily Numeracy – This scope is not only a way for students to work on their flexibility in thinking about numbers and strategies, but it also gives the class an opportunity to listen and discuss math in a structured way as a community of learners.” 

In addition, within each Explore in a Scope, Language Supports highlights suggestions to involve different reading levels. Examples include:

  • Scope 6: Positive Rational Number Operations, Explore, Explore 5–Multiply Multi-Digit Decimal Numbers, Language Acquisition Supports states,  “Beginner: Prior to the lesson, show students a zoomed-in image of a grocery store receipt. Circle the word tax on the receipt and explain to the class what taxes are. Ask students: What kinds of things are taxed? Do you think there should be taxes? etc. Explain that they will calculate the taxes of food items in this Explore. Intermediate: As a pre-lesson activity, show students a zoomed-in image of a grocery store receipt. Circle the word tax on the receipt and explain to the class what taxes are. Show students a list of things that are taxed in the United States. Then split students into groups and have them create a list of pros and cons of taxes. Advanced: As a pre-lesson activity, show students a zoomed-in image of a grocery store receipt. Circle the word tax on the receipt and explain to the class what taxes are. Show students a list of things that are taxed in the United States. Then split students into groups and have them create a list of pros and cons of taxes. Then divide the class in two and have a class debate about taxes.”

  • Scope 9: Equations and Inequalities, Explore, Explore 3–Write and Model Inequalities, Language Acquisition Supports states, “Beginner: As a pre-lesson activity, students will be given a collection of cards with differently sized monsters, some of which will be duplicates. They will be given 3 cards with the greater than, less than, and equal symbols. Have students flip over two monster cards at a time and compare the size of the monster on the first card to the monster on the second card using one of the symbol cards. Intermediate: As a pre-lesson activity, students will draw a number line that goes from 1 to 6. They will roll dice twice and compare the size of the first number rolled with the second number rolled. They will record their inequality on a sheet. Students can use the number line as a reference. Advanced: As a post-lesson activity, students will create five drawings, each representing a type of inequality or equality: greater than, less than, greater than or equal to, less than or equal to, and equal.”

  • Scope 10: Ratios, Rates, and Unit Rates, Explore, Explore 2–Ratio Tables and Graphs, Language Acquisition Supports states, “Beginner: As a pre-lesson activity, discuss the word ratio and provide examples with pictures. Have the students write the definition and create and illustration for the word ratio. Intermediate: As a pre-lesson activity, discuss the word ratio and provide examples with pictures. Have the students write the definition and create vocabulary squares for the word ratio. Vocabulary squares should include the following sections: Definition, Example (math problem), Non-example (or antonym), and Image (or drawing). Provide students with the definitions. Advanced: As a pre-lesson activity, discuss the word ration and provide examples with pictures. Have the students write the definition and create vocabulary squares for the word ration. Vocabulary squares should include the following sections: Definition, Example (math problem), Non-example (or antonym), and Image (or drawing). Provide students with the definitions.

Indicator 3V
02/02

Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The materials reviewed for STEMscopes Math Grade 6 meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods. Examples include:

  • Scope 4: Coordinate Planes, Explore, Explore 2–Reflections on a Coordinate Plane, Description states,  “Students will work with a city map and find locations of buildings to determine the relationship between the signs of numbers and locations in quadrants. Students will determine ordered pairs that show reflections across one of the axes.” Materials, “Printed: 1 Student Journal (per student); 1 Set of Building Location Cards (per group); 1 Exit Ticket (per student). Reusable: 2 Quart-sized resealable bags (per group); 1 Permanent marker (per class); 1 Set of colored pencils (per group). Consumable: 3 Card stock pages (per group, optional); 1 Large piece of white butcher paper (per group).” Preparation, “Print a set of the Building Location Cards for each group. Optionally, print on card stock and laminate for durability. Cut out Building Location Cards Part I, and place in a resealable bag labeled “Part I” for each group. Cut out Building Location Cards Part II, and place in a resealable bag labeled “Part II” for each group.” Procedure and Facilitation Points, “Give a set of colored pencils, the coordinate plane on butcher paper, and a Part I bag of the Building Location Cards Part I to each group.”

  • Scope 9: Equations and Inequalities, Explore, Explore 2–Write and Solve Equations, Description states,  “Students will write and solve equations using properties to find the value of the variable.” Materials, “Printed: 1 Student Journal (per student); 1 Set of Daily Deals Cards (per group); 1 Exit Ticket (per student). Reusable: 1 Projector or document camera (per class); 1 Resealable bag (per group).” Preparation, “Print one copy of the Daily Deals Cards per group. If desired, print on card stock and laminate for future use. Cut out the Daily Deals Cards, and place them in a resealable bag for each group. In the Procedure and Facilitation Points section it states “Give a set of Daily Deals Cards to each group.”

  • Scope 10: Ratios, Rates, and Unit Rates, Explore, Explore 2–Ratio Tables and Graphs, Description states, “Students will reason, analyze, and create tables and graphs of ratios.” Materials, “Printed: 1 Student Journal (per student); 1 Set of Purchasing Fruit Bushes Cards (per group); 1 Exit Ticket (per student).” Preparation, “Print one set of Purchasing Fruit Bushes Cards for each group. If desired, print on card stock and laminate for future use. In the Procedure and Facilitation Points section it states "Give a Student Journal to each student and the Purchasing Fruit Bushes Cards – Part I to each group.”

Criterion 3.4: Intentional Design

Read

The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.

The materials reviewed for STEMscopes Math Grade 6 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards; include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other; have a visual design that supports students in engaging thoughtfully with the subject that is neither distracting nor chaotic; and provide teacher guidance for the use of embedded technology to support and enhance student learning. 

Indicator 3W
Read

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.

The materials reviewed for STEMscopes Math Grade 6 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards, when applicable. 

The entire STEMscopes program is available online, and this review was conducted using the online materials. Throughout the Scopes and related activities and lessons, students are able to access the eBook for their grade level. Additionally, any assessments can be completed online. A tab on the website entitled, How to Use STEMscopes Math, provides videos the teacher can watch to learn about a variety of options available online. Virtual manipulatives are available throughout the K-8 program as well. Videos and Powerpoint presentations are available for the teacher to use when teaching a strategy to students. Teachers can also access blackline masters for exit tickets, assessments, and student tools on the website. 

Indicator 3X
Read

Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

The materials reviewed for STEMscopes Math Grade 6 include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

The program provides an opportunity for students to submit work through the website to the classroom teacher. Additionally, students can complete assessments digitally through the site. This allows some of the work/assessments to be auto scored by the site. Teachers can override any decisions made by the site’s scoring. Teachers also can send feedback on assignments and assessments to each student individually. In the Help section, the program provides a video as well as a handout to guide teachers through assigning and evaluating content. Examples include:

  • STEMscopes Help, Teacher Tools, STEMscopes Help Series, Assigning Content states, “Once you have classes in your STEMscopes account and your students are in your classes, you can assign material from STEMscopes to your students. They can then access under their own login and submit work to you online. Step 1: Log in and go to the Scopes tab and choose the lesson you want to assign content from. Step 2: Click on the student activity you want to assign. On that page, you will see the green Assign To Students button. Note that when you are in the orange teacher sections, you will not see that button. Click Assign to Students. Step 3: You will see a blank New Assignment page. You can now fill in the drop down menus for all the sections for your account. Then, assign to all or certain individual students within your section. Toggle your start/due dates (not required). Your assignment will not open (students see in their account) until that start date. You can then add labels that can help you/your students find certain assignments (see “Lab” example in help video). You can use your note for students portion (not required) to add notes or even to provide directions/guidance for your assignment and students will see this when they click on the assignment. Click on the green Add this Assignment button to assign. Student View of Content, Step 1: Once students log in, they will see their assignments from their teacher. Note the tags that help them search for a particular assignment. Students can click on an assignment to get started. Step 2: Once in an assignment, students can read, click to type their answers, use a drawing tool to answer questions, and click on multiple choice answers. Note students can enlarge text, use text to speech feature, highlight text, use comments & turn on dictionary mode for assistance. They can click the Save button to save their work and close, or if they’re finished, click the green Turn In button to submit. Teacher View of submitted content, Step 1: Once a teacher logs in, they will see the Student Activity feed on the lower right. It will show the name of the student(s) who completed work, title of the content, and time completed. Teachers can click on the assignment they want to view and/or grade. Step 2: After clicking on the assignment, teachers will see the information related to that assignment. If it was an auto-graded assignment the grade will appear along with how long it took the student to complete the assignment and when they turned it in. Teachers can then see individual results by clicking on the View Results button. Teachers can have students retake assignments by clicking on the Reset button. Teachers can also edit their assignment via the Edit Assignment button or archive the assignment via the Archive button.”

  • STEMscopes Help, Teacher Tools, STEMscopes Help Series, Evaluating Content states, “...Not all assignments are exactly the same. Some are autograded on the website and some are open-ended and the teacher will have to go in and assign a grade to them. Some are submitted for reference to show that they were done. One example of this is the Picture Vocabulary. Notice that it says “no” for graded, which means Picture Vocabulary doesn’t have anything for students to submit for grading (see the check mark as completed along with time spent and date completed). The Reset button will reassign it to the student and make it reappear on their end. A multiple choice assessment, however, is graded automatically. When a teacher clicks on the assignment, they’ll see all the information about the assignment: 1. Start/due dates; 2. Who assigned to; 3. Autograded checked off; 4. Average for the assignment; 5. The element assigned; 6. Which section is assigned to; 7. Option to view standards; 8. Option to Edit Assignment; 9. Archive the assignment. Teachers will see all students in the section, their status for the assignment, their grade (autograde feature), how long it took them to complete the assessment, when it was submitted, and buttons to see how they performed or to reset their assignment. When viewing results, you’ll notice the correct answers are green and the student in this example chose the correct answer. Teachers can go in and edit the credit awarded by simply clicking on the number and changing the grade (for example, to give partial credit). Teachers can also provide feedback to the students via the Note box. Once the teacher has made all notations, click the green Save button and the blue Close button. For whatever reason, to return the assessment to a student, click the red Return button and you can type in your instructions for the student and click the red Return button again. This student will update in your list with no grade and a gray Returned to student box. In this assignment snapshot, teachers can see all the questions on one screen, the percentage of correct/ incorrect answers, which standard(s) the question is attached to, and which students answered incorrectly. Missed standards will be listed at the bottom of the page. This allows the teacher to quickly see who needs help and which standard(s) may need reteaching/review. For other assignments, there are some things you have to grade by putting in a score or because they are open-ended questions. For example, this student below completed an assignment and submitted it to the teacher. The teacher will see a P in the grade column which means pending. The teacher needs to go in and assign a grade to the student’s work. To do this, click the gray Grade button to pull up the student’s work. There you can assign points based on the correct answers that are provided and make comments for the student. When done, click the green Save button and then the blue Complete button. Where you saw the P in the grade column should now change to a numerical grade based on the student’s answers. Students will not be able to see grades or notes until you click on the green Release Feedback button just above the list of their names on the main assignment page. The button will then turn orange and say Revoke Feedback. If a teacher needs to make changes, edit/add comments they can click that button and complete the process and release feedback when done. Teachers can view assignments given to multiple sections via the Students tab and click on the Assignments tab. Here, you’ll see a master list of assignments and how many sections that the assignment/assessment was given to. You can click on the items on the left to be taken to the main screen for each to begin grading/view performance.”

Indicator 3Y
Read

The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

The materials reviewed for STEMScopes Math Grade 6 have a visual design (whether in print or digital) that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

There is a consistent design across the K-8 grade levels. For each grade level, the website is formatted in a similar way. Each grade level starts with a link to the Teacher Toolbox, which provides overarching information and guidance. That is followed by a link, STEMScopes Math: Common Core Kindergarten Teacher Resources. This link provides a Scope and Sequence for the grade level, vertical alignment charts, lesson planning guides, as well as assessment alignment documents. The following link, How to Use STEMScopes Math, provides videos for the teacher to view to learn about tools and options available within the program. Launch into Kindergarten provides an overview of the curriculum at the grade level. Fact Fluency and Daily Numeracy links follow. A link to each Scope in the grade level follows. The Scopes are set up with the same tabs: Home, Engage, Explore, Explain, Elaborate, Evaluate, Intervention, and Acceleration. The materials within these tabs are clearly labeled and concise. Assessments can be completely virtually or printed, and both styles provide ample work space. 

The Help section of the web page provides guidance to teachers in navigating the site. Help, Curriculum Navigation, STEMScopes Help Series, Curriculum Navigation states, “There are a variety of resources available to teachers here to facilitate the instruction of the content. First of all, STEMScopes is built on the 5E model which is evident on the dropdown toolbar above. There is also I and A for Intervention and Acceleration. Above that you see labels for the lesson topic, grade level, and standard(s). On the right, you’ll see all the essential elements that are available to the teacher for implementing the lesson. The orange Ts are teacher elements, the blue Ss are for student elements, and the ESP means the element is available in Spanish. You can, however, visit some elements (this example is on the Explore tab, Explore Student Materials) and there will be a Ver en español button. Clicking on this will translate most of the page from English to Spanish. Another thing we offer is on the teacher elements. Our content is online where students can read, complete the work, and submit it to teachers within the site, but there are downloadable versions of the content too. This is accessed by clicking on the Print Version button on the right of the page. When you click on it, it will download/open as a digital PDF that you can make copies of or email to parents if needed. Also, you will see the customization bar at the top of every page. It floats down with you as you scroll and can help teachers and students with text sizing, text-to-speech, highlighting text, inserting comments to the page/to text, and defining words. You can get more in-depth tutorials for these features via their individual videos/help sheets. Each teacher element will have the following buttons: Assign to Students: Click to assign the element to your sections to work on in class, as homework or intervention. Add to Planner: Click to add the element to your planner when mapping out how you will teach the Scope. Bookmark Element: Click to bookmark the element to your home page for quick access. 1. Text sizing 2. Text-to-speech 3. Highlighting feature 4. Comment feature 5. Dictionary feature Finally, on the main Scopes page, you will see three resources that you can use. The Teacher Toolbox can help with your planning, lab resources, and lesson matrixes. The Visual Glossary provides a media library of science terminology for teachers and students. STEMcoach in Action is a free professional development resource for teachers. It’s worth noting that not all Scopes look the same and, consequently, some elements may look a little different depending on what grade level you’re subscribed to.”

Students materials are available in printed and eBook form. Both versions include appropriate font size, amount and placement of direction, and space on the page for students to show their mathematical thinking. 

Indicator 3Z
Read

Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The materials reviewed for STEMscopes Math Grade 6 provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The materials reviewed were digital only. In each grade level, a section entitled, How to Use STEMscopes Math, provides videos teachers can use to learn about the options available online. Each Scope also provides virtual manipulatives for teachers and students to use to enhance learning. Students can also complete assessments throughout the program online. Facilitation Tips within each Scope’s Teacher Guide provide helpful hints to the teacher as they progress through the Scope.